THE 


ELEMENTS 


PERSPECTIVE. 

BY 


SIMEON  DE  WITT. 


ALBANY i 

PRINTED  BY  H.  C.  SOUTHWICK. 
No.  94,  State-Street. 


1813. 


DISTRICT  OF  NEW-YORK,  or. 

Be  it  remembered,  that  on  the  first  day  of  January,  in  the  thirty- 
eighth  year  of  the  Independence  of  the  United  States  of  America, 
Simeon  DeWitt , of  the  said  District,  hath  deposited  in  this  office  the  title 
of  a Book,  the  right  whereof  he  claims  as  author,  in  the  words  following^ 
to  wit  : 

“ THE  ELEMENTS  OF  PERSPECTIVE.  By  Simeon  DeWitt/7 
lu  conformity  to  the  act  of  Congress  of  the  United  States,  entitled 
“ An  act  for  the  encouragement  of  learning,  by  securing  the  copies  of 
maps,  charts  and  books,  to  the  authors  and  proprietors  of  such  copies, 
during  the  time  herein  mentioned.”  And  also  to  an  act,  entitled,  “ An 
act  supplementary  to  an  act,  entitled  “ An  act  for  the  encouragement  of 
learning,  by  securing  the  copies  of  maps,  charts  and  books,  to  the  authors 
and  proprietors  of  such  copies,  during  the  times  therein  mentioned,  and 
extending  the  benefits  thereof  to  the  arts  of  designing,  engraving  and  etch- 
ing historical  and  other  prints.” 

THERON  RUDD, 

Clerk  of  the  District  of  Nerv-York . 


PREFACE. 


It  will  be  seen  by  the  Introduction  to  this  Trea- 
tise, that  the  Author’s  principal  aim  in  publishing  it  is, 
to  have  Perspective  introduced  among  the  studies  of 
a liberal  education.  His  motive  is  a sincere  convic- 
tion that,  if  this  end  be  accomplished,  he  will  have 
done  a service  to  the  community.  With  this  view, 
he  has  taken  some  pains  to  make  his  subject  an  ob- 
ject of  attention,  by  giving  it  an  attractive  appear- 
ance, and  shewing  the  many  respects  in  which  it  may 
have  a wholesome  influence  on  the  morality  and 
happiness,  as  well  as  on  the  usefulness  of  men  as  mem- 
bers of  society.  The  style  and  manner,  which  he 
has  purposely  assumed  to  effect  this,  he  leaves,  as  a 
matter  of  experiment,  to  the  animadversions  of  critics, 
with  a perfect  indifference  for  the  result ; for  the  ac- 
quisition of  literary  fame  never  yet  entered  his  most 
chimerical  dreams,  and  he  most  certainly  will  never 
put  himself  in  pursuit  of  that  phantom,  or  make  an 
effort  to  seize  it,  how  much  soever  he  may  be  pleas- 
ed to  see  others  in  the  chase  or  gratified  by  their  suc- 
cessful exertions. 

His  method  of  explaining  the  Art  of  Perspective, 
as  it  is  different  from  that  of  preceding  writers  on  the 
same  subject,  and,  as  he  believes,  better  adapted  to 
the  habits  of  students  passing  through  a Mathemati- 
cal course,  he  flatters  himself  will  more  effectually 
fix  their  attention  to  it,  and  enable  them  to  acquire  a 


IV 


PREFACE. 


knowledge  of  it  with  more  ease.  Prolixity,  it  will  be 
observed,  has  been  avoided  as  much  as  possible,  with- 
out neglecting  a due  regard  to  perspicuity  ; and  the 
Examples  have  been  limited  in  number  to  what  was 
indispensable  for  illustrating  the  Rules:  Whoever 
makes  himself  master  of  the  Elements , will  not  need 
any  more  to  instruct  him  in  the  drawing  of  objects  of 
every  kind ; and  teachers  will  be  able  to  multiply 
them  at  pleasure. 

How  far  the  author  has  succeeded  in  his  views  must 
be  left  to  the  decision  of  judges  more  competent  and 
less  interested  than  himself.  Aware  of  the  false  esti- 
mate we  are  prone  to  make  of  our  own  productions, 
and  the  extravagant  value  we  generally  set  on  favo- 
rite things,  however  diminutive,  he  is  far  from  being 
sanguine  that  others  will  view  his  subject  with  the 
same  impressions  of  its  importance,  or  that  this  work 
will  meet  with  the  unqualified  approbation  of  those 
who  are  best  able  to  form  a correct  opinion  of  its  me  • 
rits.  He  is  not,  however,  without  hopes  that  the 
charms  of  his  favorite  will  obtain  her  a permanent 
place  in  our  seminaries  of  learning,  and  that  she  will 
yet  be  cherished  as  a beautiful,  worthy,  little  sister  of 
the  sciences.  If  so,  he  will  be  happy  to  think  that 
what  was  his  amusement  has  become  productive  of  a 
public  benefit. 

As  he  does  not  calculate  on  any  pecuniary  gain 
from  this  publication,  but  rather  the  reverse,  and  as 
its  limited  scope,  and  the  littleness  of  its  subject,  for- 
bid the  surmise  that  he  is  prompted  by  the  ambition 
of  acquiring  reputation  by  it,  he  hopes  full  credit  will 
be  given  to  the  avowed  integrity  of  Iris  motive.  He 


PREFACE. 


v 


therefore  claims  the  right  of  an  exemption  from  the 
suspicion  of  self-interest,  while  he  calls  on  those  who 
superintend  the  American  institutions,  dedicated  to 
the  Arts  and  Sciences , to  give  their  patronage  to  works 
of  this  kind,  which  from  the  very  nature  of  them,  can 
be  in  demand  with  but  a small  portion  of  Readers, 
and  which  cannot  therefore  be  brought  before  the 
public  without  individual  sacrifice,  or  that  patronage 
which  can  be  effective.  Why  so  few  scientific  works 
are  seen  as  the  product  of  America,  is  doubtless  ow- 
ing to  this  cause,  and  not  to  a sterility  of  genius,  or  a 
want  of  adequate  talents.  This  ordinary  discourage- 
ment may  not  be  a matter  of  serious  consideration,  in 
the  present  instance,  with  the  writer  of  this  Treatise  ; 
but  with  many  it  would  be  an  imperious  veto  against 
the  bringing  of  their  productions  into  the  world,  were 
the  merit  of  them  ever  so  great,  or  should  the  acqui- 
sition of  them  be  ever  so  invaluable. 

This  call  is  addressed  to  the  Patriotism  of  our 
Country  ; a country  which,  for  many  reasons,  ought 
to  be  eminently  proud  of  its  Independence,  and  omit 
no  opportunity  of  giving  it  a more  decided  and  per- 
fect character : But  this  cannot  be  expected  without 
having  the  spirit  and  munificence  of  the  Maoenases 
and  the  Medici  of  other  nations  emulated  in  our 


own. 


V 


I - f f . * - 


Digitized  by  the  Internet  Archive 
in  2015  ’ 


\ 


https://archive.org/details/elementsofperspeOOdewi 


INTRODUCTION. 


EVER  since  I have  been  acquainted  with  Perspect- 
ive, that  elegant  and  very  useful  little  branch  of  the 
Arts,  sprung  from  the  Science  of  Mathematics,  has 
appeared  to  me  too  much  neglected  in  the  education 
of  youth.  While  public  seminaries  profess  to  make 
their  pupils  acquainted  with  the  whole  circle  of  the  sci- 
ences, and  give  them  the  accomplishments  requisite  for 
entering  the  world  with  respectability  and  prospects 
of  usefulness,  this,  strange  as  it  may  seem,  receives 
generally  no  more  notice  than  if  it  had  never  been 
discovered.  Perhaps  the  reason  is,  because,  few  hav- 
ing seen  it  treated  as  an  appendage  to  Mathematics,  it 
is  considered  as  belonging  exclusively  to  the  Draw- 
ing-Master, and  therefore  unbecoming  a place  in  a 
learned  institution,  when,  in  fact,  the  Drawing-Mas- 
ter, although  well  qualified  to  be  useful  in  his  station, 
may  know  nothing  of  its  principles,  and  therefore  can- 
not teach  it  : or  perhaps  it  is  ranked  among  those 
things  which  serve  only  for  idle  amusement ; or  it  may, 
be  because  it  is  thought  that  drawing  can  be  suf- 
ficiently learnt  without  it,  as  some  learn  the  practice 
of  Music,  without  knowing  any  thing  of  the  Gamut 
or  Notes. 

It  is  to  remove  such  misconceptions  and  prejudices 
and  to  do  justice  to  the  merits  of  this  art,  that  I have 


INTRODUCTION. 


viii 

been  induced  to  unveil  its  countenance  anew  to  the 
public,  and  to  give  it  a dress  different  from  any  in 
which  it  has  yet  appeared.  I shall,  in  this  introduc- 
tion, shew  its  usefulness,  and  then  explain  and  demon- 
strate its  principles  and  the  practical  rules  deductible 
from  them. 

All  that  I have  ever  seen  on  the  subject,  has  ap- 
peared unsatisfactory  to  me.  I Lave,  therefore,  not 
followed  the  plan  of  any  previous  author,  but  have  as- 
sumed a method  which  I conceived  best  calculated  to 
explain  the  principles  of  the  art,  and  to  develope  its 
elements  by  a regular  mathematical  process ; which, 
I hope,  will  give  such  a view  of  it  as  that  it  shall  ap- 
pear not  unworthy  of  being  made  a task  even  for  stu- 
dents under  the  professors  of  a University.  The 
little  time  it  will  take,  for  any  young  gentleman,  in  a 
regular  course  of  education,  to  make  himself  master 
of  it,  compared  with  the  very  great  use  he  may  find 
in  it,  carries  to  my  mind  an  irresistible  argument  for 
its  adoption  as  an  indispensable  part  of  public  instruc- 
tion. Projections  of  the  Sphere,  Conic  Sections  and 
Spherical  Trigonometry,  are  indeed  necessary  step- 
ping-stones to  the  higher  branches  of  science,  but  they 
are  of  little  practical  use  to  most  students  after  their 
emancipation  from  College  ; and  I will  venture  to  say, 
of  less  benefit  on  the  whole,  than  this  study  would  be, 
were  it  made  equally  general.  It  opens  a path  into 
which  strong  allurements  invite  the  reasoning  facul- 
ties. It  is  therefore  well  calculated  to  lead  them  into 
a cheerful  submission  to  that  extent  of  discipline  which 
is  held  necessary  for  rearing  them  to  maturity  ; and 
this  consideration  alone  gives  it  a stamp  of  value  that 


INTRODUCTION. 


k 

entitles  it  to  more  than  common  regard.  Were  no 
other  purpose  contemplated — were  it  not  even  intend- 
ed ever  to  apply  it  to  practice,  still  its  use  in  this  re- 
spect  would  amply  justify  its  adoption. 

The  Americans  are  an  inventive  people  ; perhaps 
more  so  than  any  other  existing.  We  have  reason 
to  think  so  from  the  number  of  inventions  made  pub- 
lic and  applied  to  useful  purposes  within  a few  years : 
And,  without  arrogating  to  ourselves  any  superiori- 
ty of  intellect,  the  cause  may  be  traced  to  our  more 
favorable  circumstances ; especially  to  the  facility 
with  which  a respectable  education  and  the  means  of 
comfortable  subsistence  may  be  procured,  and  which 
leaves  leisure  to  the  mind  to  wander  through  the 
mysterious,  unfathomable  repositories  of  possible 
things ; to  the  boundless  field  of  improvement  be- 
fore us,  and  to  the  scarcity  of  labouring  hands,  which 
acts  as  a constant  stimulus  to  resort  to  the  mechani- 
cal powers,  and  every  other  attainable  aid,  to  supply 
the  deficiency. 

In  aid  of  the  inventive  faculty,  Perspective  or 
rather  Draw  ing,  of  which  it  is  the  foundation,  serves 
a twofold  purpose.  It  creates  habits  of  forming  clear 
and  distinct  ideas  of  complex  objects,  with  the  rela- 
tive bearings  of  all  their  parts,  whether  such  objects 
have  been  presented  to  the  eye,  or  be  only  crea- 
tures of  the  mind,  and  changed  to  every  shape  and 
position,  in  order  to  ascertain  which  will  best  answer 
a meditated  purpose.  The  imagination  becomes  so 
far  improved  by  it,  that  the  models  it  forms  are  as 
complete  as  those  made  of  material  substances.  But 
its  most  useful  office  is  to  give  substance  and  visibili- 
ty to  those  aerial  shapes.  The  productions  of  the 

2 


introduction. 


X 

creative  mind  grow  under  the  pencil  till  they  result 
in  wonderful  systems,  endowed  with  powers  to  pro- 
duce effects  of  incalculable  benefit  to  man.  I have 
no  doubt  that,  for  the  want  of  this  art,  many  a one, 
who  had  got  on  the  track  of  some  useful  discovery, 
has  lost  his  way  in  the  pursuit  and  been  necessitated 
to  abandon  it ; as  the  strongest  mind  would  be  oblig- 
ed to  discontinue  the  investigation  of  some  problems, 
without  the  aid  of  algebraic  characters,  that  keep 
the  whole  process  of  his  reasoning  continually  before 
his  eyes,  and  render  his  progress  to  the  conclusion 
practicable  and  easy. 

Without  this  art  moreover,  it  would  be  impossible 
to  communicate  some  discoveries,  and  make  them  in- 
telligible, even  to  the  artists  who  alone  can  bring 
them  into  use. 

How  often  does  it  happen  that  the  agriculturalist 
or  the  manufacturer  requires  implements  or  machine- 
ries which  cannot  be  explained  without  accurate 
drawings ! Such  agriculturalist  and  manufacturer  may 
have  received  a liberal  and  even  a polished  education, 
and  why  cannot  they  give  the  requisite  description  ? 
It  is  because  this  art  was,  most  undeservedly,  consi- 
dered as  too  insignificant  or  too  useless  to  be  taught, 
and  therefore  they  were  left  in  total  ignorance  of  the 
beauties  and  powers  of  its  language.  But  the  in- 
stances in  which  a knowledge  of  it  would  be  found 
at  least  a convenient  thing , even  where  it  might  not  be 
wanted  as  a professional  qualification,  cannot  be  enu- 
merated. 

That  drawing  may  be  learnt  to  a certain  extent, 
without  a knowledge  of  perspective,  is  granted ; so 
may  trigonometry,  surveying  and  navigation  be 


INTRODUCTION. 


y* 

learnt  by  committing  some  rules  to  memory.  But  is 
this  a competent  education?  Would  it  be  sufferable 
in  a public  seminary  ? Could  any  student,  possessed 
of  ordinary  ingenuity,  undergo  the  drudgery  of  piling 
on  his  memory  rules  upon  rules  of  which  he  knows 
not  the  reason  ? Knowledge  thus  acquired  is  deserv- 
edly held  in  contempt  as  mere  smattering,  and  a dis- 
reputable mimicry  of  science,  and  the  pretenders  to 
it  considered  as  incapable  of  rising  to  a respectable 
eminence. 

> In  drawing,  through  all  the  grades  of  the  profes- 

sion, from  the  planner  of  architectural  works  to  the 
historical  painter,  an  acquaintance  with  perspectiVe 
is  necessary ; and  especially  in  those  performances 
in  which  the  joint  powers  of  genius  and  fancy  are  to 
be  displayed  ; there  it  becomes  emphatically  indis- 
pensable.* 

To  the  traveller  this  art  is  invaluable.  With  those 
who  have  ample  means  for  the  purpose,  it  is  a lauda- 
ble practice  to  send  their  sons,  after  finishing  their 
ordinary  course  of  education  at  home,  to  visit  diffe- 
rent parts  of  the  world,  in  order  that  they  may  ac- 
quire a knowledge  of  it  which  cannot  be  acquired 
from  books,  and  that  they  may  see,  in  the  displays  of 
the  human  character  in  its  varieties,  in  the  works  of 
art,  and  in  the  appearances  and  productions  of  na- 
ture, in  different  regions,  exemplifications  of  what 
they  had  been  taught  in  the  retirement  of  study,  with 
the  view  that  the  information  thus  acquired  may  be 
preserved  to  assist  them  in  their  future  services  to 
their  country.  But  every  reader  would  anticipate 
me,  should  T undertake  to  mention  how  many  things 
there  are  which  in  a little  time  will  grow  dim  on  the 
* See  note  A. 


INTRODUCTION* 


xii 

traveller’s  memory,  and  how  many  which  it  will  be 
impossible  for  him  to  make  known  tb  others,  or  even 
to  preserve  in  his  own  recollection,  without  availing 
himself  of  this  art.  Without  it  What  account  would 
De  Non  have  brought  from  Egypt  ? His  verbal  de* 
scriptions  of  that  interesting  country,  the  cradle  of 
the  human  intellect,  would  doubtless  have  been  as 
accurate  as  language  could  make  them ; but,  like  the 
descriptions  of  the  enchanted  castles  of  novelists,  or 
even  like  the  description  of  the  Turkish  seraglio,  by 
Clarke,  they  would  have  only  filled  the  brain  w ith  a 
confused  mixture  of  obscure  and  mutilated  ideas, 
and  tortured  it  with  painful,  perplexed,  unavailing 
efforts  at  distinct  perception.  But  it  wTas  otherwise 
With  our  traveller.  He  brought  back  with  him  the 
perfect  resemblances  of  what  he  saw,  and  has  given 
us  a view  of  the  mansions,  the  temples  and  the  Gods 
of  the  Pharaos’  who  flourished  in  ages  buried  deep  in 
the  dark  bosom  of  antiquity*  and  of  a race  become 
venerable  by  their  affinity  to  the  infancy  of  the 
world. 

He  who  cannot  mould  and  group  his  ideas  in  dis- 
tinct vivid  images,  and  pencil  them  on  his  fancy  with 
the  skill  of  a painter,  must  never  dream  of  chaplets 
about  his  temples  for  exploits  in  the  field  of  Poetry. 
This  art  is  therefore  important  also  in  that  depart- 
ment of  genius.  And  even  in  prose-rhetorick,  mak- 
ing pretensions  to  merit,  how  often  do  we  meet  w7ith 
metaphorical  images  of  monstrous  shapes  and  the 
most  incongruous  composition ! As  such  must  ever 
be  disgusting  to  a correct  critical  taste,  they  could 
never  be  admitted  into  the  productions  bf  one  ac- 
quainted with  the  rules  of  symmetry,  and  that  chaste* 


INTRODUCTION. 


xiii 

harmonious  arrangement  of  imagery,  which  perspec- 
tive familiarizes  to  the  mind. 

In  the  allusions  of  Homer,  Virgil,  Shakspeare  and 
Milton,  we  see  things  as  distinctly  as  if  they  were 
presented  to  us  in  a finished  picture.  On  the  contra- 
ry, we  see  in  much  of  modern  composition,  the  fi- 
gures intended  to  be  introduced  scarcely  emerging 
from  a fog  impervious  to  the  utmost  efforts  of  intel- 
lectual vision,  or  so  mis-shapen,  or  thrown  upon  each 
other  in  such  confusion,  that  they  resemble  the  odd 
compound  of  the  Zodiac,  rather  than  those  simple, 
plain,  complete,  w ell  selected  and  well  arranged  ob- 
jects most  proper  to  make  deep,  lively  and  agreeable 
impressions  on  the  mind.  Whoever  will  compare 
literary  works  of  universally  acknowledged  merit, 
not  depending  on  any  temporary  fashion  of  language> 
with  those  frothy  productions  which,  by  a quaintness 
of  phraseology,  a clumsy  attempt  at  rhetorical  fi- 
gures, a rhapsodical  affectation  of  passion  and  senti- 
ment, or  a ridiculous,  studied  departure  from  all  the 
rules  of  metrical  arrangement,  obtain  an  ephemeral 
currency,  will  constantly  find  this  difference. 

Nor  can  it  be  unobserved  in  how’  many  poetic  as 
well  as  prose  writers,  there  appears  too  much  of  a 
disregard  for  that  melody  and  forcible  expressive- 
ness of  sousd  of  which  our  language  is  so  happilv 
capable  ; and  which,  by  the  most  celebrated  orators 
and  poets  of  antiquity,  were  evidently  studied  to  the 
utmost  extent  of  possible  refinement.  It  is  doubt- 
less ow  ing  to  a long  continued  prevalence  of  this 
study  that,  w ith  them,  an  undefinable  latitude  in  the 
transposition  of  words,  especially  in  the  Latin  tongue, 
became  orthographically  allowable.  It  is  from  the 


XIV 


INTRODUCTION, 


same  cause  that  in  the  French  orthography,  some- 
times the  adjective  and  sometimes  the  substantive  is 
directed  to  be  the  antecedent. 

An  art  which  refines  the  sense,  that  receives  the 
harmonies  which  the  eye  transmits  to  the  soul,  cannot 
but  have  somewhat  of  a similar  effect  on  the  sense 
that  receives  the  harmonies  of  which  the  ear  is  the 
organ  of  transmission  ; and  especially  in  the  offices 
of  language,  by  which  pleasurable  ideas  and  pleasur- 
able sounds  are  simultaneously  communicated,  and 
by  a concordant  impetus,  produce  the  ultimate  effect 
to  which  its  powers  are  limited.  Drawing,  sculpture, 
music,  poetry,  and  the  poetic  qualities  of  prose,  have 
reciprocal  effects,  and  act  with  each  other  as  auxili- 
aries ; a proficiency  in  either  of  them  will  therefore 
be  serviceable  to  attainments  in  some  one,  if  not  in 
each,  of  the  others,* 

These  observations  are  made  for  the  consideration 
of  those  who  are  concerned  in  the  instruction  of 
youth,  to  assist  them  in  judging  how  far  that  preci- 
sion in  the  delineation  of  objects,  and  that  relish  for 
the  harmonies  of  proportion  which  are  acquired  by 
the  practice  of  drawing,  may  be  of  use  in  forming 
the  true  taste  of  criticism  and  habits  of  chaste  com- 
position. 

No  approaches  can  be  made  to  the  perfection 
of  Art,  without  the  habit  of  attentively  observing 
the  attributes  and  operations  of  nature,  and  a perse- 
vering study  to  imitate  them  ; and  for  this  perspec- 
tive paves  the  avenue  and  opens  the  gate.  Those 
matchless  specimens  of  taste,  the  Grecian  columns, 
which  have  mocked  the  efforts  of  a thousand  years  to 

* See  note  B. 


INTRODUCTION. 


xv 


produce  an  equal,  grew  from  observations  made  on 
the  trunks  of  trees,  and  the  shapes  and  curvatures  of 
leaves  ; and  the  finest  ornaments  of  architecture  are 
but  imitations  of  the  fruits,  flowers  and  foliage  with 
which  nature  adorns  the  earth.  Let  the  orator  attend 
to  the  gestures  of  a child,  as  soon  as  it  has  obtained 
the  command  of  its  limbs  ; or  to  the  giant  of  the 
woods,  and  the  motions  of  his  arms,  when  fencing 
with  the  winds,  and  they  will  give  him  instructive  les- 
sons in  the  practice  of  his  profession.  In  both  there  is 
that  gracefulness  and  total  absence  of  awkwardness 
which  the  most  finished  education  in  man  can  never 
attain. 

An  aptitude  and  partiality  for  drawing,  have  a ten- 
dency, more  powerful  than  any  other  bent  of  the  mind, 
to  improve  that  taste  which  qualifies  us  for  relishing 
the  beauties  of  the  Fine  Arts  as  well  as  the  beauties 
of  Nature,  and  without  which,  no  work  of  excellence 
can  ever  be  produced.  They  have  a tendency  also 
to  improve  the  Moral  Complexion  of  the  human 
soul ; for  there  is  that  affinity  between  the  beauties 
of  nature  and  the  beauties  of  morality,  that  he  whose 
sensibilities  are  alive  to  the  one,  cannot,  without  hav- 
ing unnaturally  jarring  elements  dominant  in  his 
make,  be  impassive  to  the  other. 

To  contemplate  the  wonderful  works  of  the  Cre- 
ator, the  Magnalia  Dei,  is  the  chief  purpose  of  our 
creation,  and  therefore  are  virtue  and  happiness  so 
closely  connected  with  it. 

I may  add  in  illustrating  the  usefulness  of  my  sub- 
ject, that  without  some  acquaintance  with  it  a MILI- 
TARY EDUCATION  cannot  become  perfect. 

Besides  serving  those  purposes  of  practical  utility; 
Perspective  drawing,  as  a minister  of  R ATIONAL 


INTRODUCTION. 


*vi 

AMUSEMENT,  holds  a high  station  in  the  gradua- 
tions of  merit ; and  may  almost  dispute  precedency 
with  the  poetic  muse.  Let  those  who  practice  it,  and 
those  whose  harmoniously  strung  feelings  enable 
them  to  relish  its  performances,  testify  ; to  such,  any 
observations  as  proofs  would  be  needless,  and  to 
others,  they  would  be  as  vain  as  pourtraying  the  rain- 
bow for  the  entertainment  of  the  blind. 

Amusements  must  be  had— by  the  busy  to  relieve 
them  from  the  lassitude  of  toil,  and  re-invigorate 
them  for  labor — by  the  idle,  to  fill  up  the  dreadful 
vacuities  of  time  : And  wo ! to  that  man  who  is  not 
furnished  with  harmless  resources  from  which  to 
draw  the  supply.  The  most  pitiable  object  of  our 
race  is  lie  who  is  cursed  with  an  ample  patrimony, 
without  possessing  the  talents  and  education  to  fit 
him  for  being  usefully  busy,  and  without  the  capaci- 
ty of  being  reputably  and  innocently  amused.  His 
malignant  destiny  drives  him  to  the  fraternity  of  gam- 
blers, the  resorts  of  drunkards,  or  the  haunts  of  more 
infamous  gratifications,  as  refuges  from  the  intolera- 
ble dreariness  of  a vacant  life.  An  acquaintance 
with  one  source  of  diversion  for  his  mind,  such  as  is 
here  recommended,  might  save  him  from  ruin. 

And  why  do  we  see  so  many  of  the  lovelier  part  of 
the  human  race  sacrifice  the  best  of  their  time,  or  so 
much  of  it  as  can  be  spared  from  other  noxious  re- 
creations,  to  the  DEMON  of  ROMANCE,  have 
their  delicate,  susceptible  minds  irremediably  poison- 
ed by  that  pestiferous  trash,  which,  under  the  deno- 
mination of  Novels , is  poured  upon  the  world;  and, 
by  indiscriminately  and  incessantly  swallowing  those 
deleterious  opiates,  have  their  judgments  deranged. 


INTRODUCTION. 


xvii 

and  their  mental  appetites  so  utterly  vitiated,  as  to  re- 
volt from  the  natural  aliment  of  rational  souls  ? It  is 
because  for  their  employment,  selections  have  been 
made  of  frivolous  studies,  and  readings  calculated 
merely  to  fascinate  them,  or  to  embellish  their  scanty 
acquirements  with  the  tinsel  glitter  of  mock  orna- 
ment. They  have  had  no  guide  to  direct  their  par- 
tialities to  substantial  improvements,  and  those  acqui- 
sitions which  give  power  to  the  lovely,  unsophisticat- 
ed, native  blandishments  of  the  sex.  They  have  had 
no  friend  to  bend  their  habits  to  employments  worthy 
of  the  rank  they  hold  in  the  scale  of  being,  and  tend- 
ing to  ennoble,  as  well  as  to  sweeten,  the  amiable  dip- 
ties,  which  it  is  their  proud  prerogative  to  claim  as 
exclusively  theirs  ; and  especially, 

“ Well  ordered  home  man’s  best  delight  to  make.” 

When  we  contemplate  the  illimitable  field  which  a 
beneficent  Providence  has  opened  for  the  activity  of 
man,  and  the  delightful  incentives  that  press  us 
through  all  its  avenues,  it  seems  incredible  that  any 
one  should  be  found  to  loiter  on  its  confines  in  inglo- 
rious indolence.  And  yet  we  behold  multitudes  who 
can  scarcely  find  any  thing  to  pursue  to  which  they 
are  not  impelled  by  stimulants  possessed  in  common 
with  the  brutal  race.  Habits  suffered  to  acquire  a 
spontaneous  growth,  the  criminal  neglect  of  early 
discipline  in  the  proper  duties  of  life,  cruel  indulgen- 
ces of  a depraved  propensity  to  idleness,  and  a wrant 
of  attention  to  the  cultivation  of  those  inlets  of  ration- 
al delight,  so  bounteously  provided,  for  animating 
and  cheering  Us  on  the  journey  of  life,  bring  on,  with 
an  accelerated  speed,  that  fatal  apathy,  which,  to  the 
miserable  sufferer,  blasts  all  the  beauties  of  creation. 

3 


INTRODUCTION. 


xtiii 

It  is  the  destiny  of  man,  fixed  unalterably  in  the 
councils  of  eternal  wisdom,  that  he  must  be  employ- 
ed ; he  must  have  some  object  of  pursuit  or  be  mise- 
rable ; and  it  is  a wise  provision  in  the  laws  of  na- 
ture, that  he  has  innumerable  wants  to  coerce  him  in- 
to the  road  of  happiness,  and,  like  the  flaming  sword 
of  paradise,  drive  him  to  fields  where  he  must  labor 
or  die ; where  corporeal  toil  or  mental  energy  only 
can  save  him  from  the  wretchedness  of  his  doom. — 
The  condition  of  one  fortuitously  placed  above  the 
necessity  of  summoning  all  his  powers  into  action,  is 
an  unnatural  condition,  and  therefore  cannot  be  hap- 
py ; unless  education,  like  a spirit  from  another 
world,  rouse  up  in  him  the  dormant  enthusiasm  that 
soars  above  the  common  track  of  human  actions,  and 

aims  at  nobler  ends  than  the  subservience  of  ordinary 

* 

wants. 

HAPPINESS  and  IDLENESS  can  never  become 
associates.  Alan  must  act  or  suffer.  To  prepare 
one  for  a happy  as  well  as  for  a useful  life,  it  is  there- 
fore necessary  to  furnish  him  with  as  many  as  possi- 
ble of  those  means  which  the  paternal  goodness  of 
Heaven  has  provided,  and  permitted  us  to  use,  for 
keeping  in  employ  the  active  instinct  of  our  nature, 
when  not  demanded  by  imperative  duties,  in  gratifi- 
cations compatible  with  its  dignified  elevation  above 
the  level  of  a mere  animal : And  among  those  means, 
that  which  is  now  recommended,  is  certainly  not  one 
of  inferior  importance  ; nay,  some  that  have  been 
honored  with  a permanent  place  in  the  systems  of 
fashionable  education,  can  by  no  means  boast  of  equal 
pretensions. 

Perspective  drawing,  especially  that  of  Landscape, 


INTRODUCTION. 


xix 


gives  him  who  is  made  familiar  with  its  principles 
and  practice  a new  and  deeper  interest  in  the 
APPEARANCES  of  THINGS.  By  it  he  becomes 
habituated  to  discriminating  views  of  their  beauties, 
and  thus  they  acquire  a superior  power  of  minister- 
ing to  his  pleasures.  In  the  aspect  of  nature,  where 
others  see  nothing  to  affect  them,  but  look  “ with 
brute,  unconscious  gaze,”*  he  sees  the  distinct  my- 
riads of  parts,  wonderfully  formed  and  put  toge- 
ther by  infinite  wisdom  to  constitute  a whole,  per- 
fect in  all  the  varieties  of  proportion,  shape,  co- 
lor, and  purpose,  and  his  sensations  are  absorbed  and 
dissolve  in  the  harmony  that  reigns  universally 
among  them.  Delight  streams  into  his  soul  from 
every  quarter  to  which  he  turns  the  contemplative 
eye.  With  rapture,  felt  in  his  bosom  alone,  he  sees, 
spreading  over  the  desolation  of  the  year  and  displayed 
in  all  the  dazzling  perfection  of  beauty,  the  infinitely 
diversified  colorings  of  the  groves,  the  fields,  the 
orchards,  and  the  gardens  of  SPRING,  with  their 
nameless  multitudes  of  animated  beings,  wakened  to 
ecstacy  by  the  spirit  of  the  season — the  boundless 
luxuriance  of  SUMMER— the  fields  of  HARVEST 
in  playful  motion  enjoying  the  balmy  respirations  of 
the  SOUTH — and  the  endless  profusion  of  AU- 
TUMN pendant  in  its  countless  varieties  of  charm- 
ing, delectable  appearances ; and  even  WINTER, 
at  every  return,  to  the  latest  period  of  life,  rekindles 
the  juvenile  joys  with  which  he  saw  its  approaches, 
braved  its  storms,  mingled  with  its  wild  elements, 
himself  as  wild,  and  exulted  in  its  sports.  With  sen- 
sations equally  charmed,  he  sees  the  beauty  of  the 
riplings  of  RIVULETS,  and  the  grace  and  majesty 

* See  note  C. 


XX  INTRODUCTION. 

of  the  billows  of  OCEAN,  moving  in  proud,  curved 
attitudes,  or  rolling  and  roaring  before  the  winds  that 
play  on  his  bosom.  With  the  etherealised  feelings  of 
enthusiasm,  he  sees  “ the  jocund  MORN  standing 
tipt  e on  the  misty  mountain  top,”  and  dilating  and 
brightening,  as  she  mounts  the  blue  vault, the  glory  of 
crimson  lustre  that  radiates  about  her ; the  SUN 
from  his  meridian  throne  pouring  “ the  vital  ocean’’ 
round  and  with  his  lights  and  shades,  giving  his 
exquisite  finish  to  the  picture  of  every  prospect, 
or  with  his  inimitable  tints,  painting  the  clouds  that 
hover  over  him  as  he  sinks  to  his  nocturnal  retreat ; 
the  MOON,  like  the  brilliant  on  the  forehead  of  fa- 
bled Diana,  suspended  among  the  STARS,  or  seated 
among  them,  as  the  QUEEN  of  NIGHT,  in  full 
splendor,  beaming  a pale,  pensive  hue  on  the  dim, 
death-like  visage  of  the  SLEEPING  WORLD — the 
ever  shifting  scenery  of  the  SKIES,  and  all  the  gor- 
geous drapery  of  HEAVEN.  These  compose  the 
seraphic  visions  of  him  whose  faculties  have  be- 
come thus  refined  and  expanded  to  their  influence. 

When  from  behind  the  western  hills,  in  awful 
form,  begirt  with  the  darkness  of  black  conglomerat- 
ing clouds,  rises  THE  TEMPEST,  and  comes  driv- 
ing on,  in  all  the  pomp  of  terrible  majesty,  with  an 
immeasurable  cataract  before  him,  lightnings  in  his 
hands,  embattled  HURRICANES  in  his  rear, 
and  the  roar  of  Heaven’s  artillery  round  him ; the 
grandeur  and  sublimity  of  the  spectacle  are  seen, 
felt  and  enjoyed  by  HIM  who  is  accustomed  to  look 
with  a perspective  eye.  And  when  again,  the  last 
rumbling  of  the  retreating  THUNDER  is  heard  in 
the  east,  and  the  relenting  clouds  hang  out  the  celes- 


INTRODUCTION. 


xxi 


tial  signal,  the  pledge  of  purposes  benign,  and  men 
gaze  at  the  gladdening  gaudy  wonder ; and  the  te- 
nants of  the  air,  the  SPIRITS  OF  MELODY  incar- 
nated, in  bands  of  millions,  fill  heaven’s  concave  with 
the  serenade,  to  welcome  the  returning  monarch  of 
day,  hushing  the  elements  and  diffusing  joy  over  the 
earth;  HE  sees  and  enjoys  the  BEAUTY  of  the 
scene. 

It  is  not  pretended  that  such  perceptions,  and  the 
sensations  they  produce,  are  exclusively  his  in  whom 
they  are  thus  cultivated ; but,  beyond  all  doubt,  to 
him  they  become  a source  of  pleasure  to  a degree , and^ 
in  some  respects,  in  a manner , with  which  others  are 
altogether  unacquainted. 

In  those  happy  regions  to  which  “ the  spirits  of  just 
men  made  perfect”  are  to  be  translated,  it  is  supposed 
that  there  are  objects  which  cannot  be  apprehended  by 
any  of  the  senses  belonging  to  man  in  his  present  stage 
of  existence,  and  that  new  senses  will  be  furnished* 
for  the  contemplation  of  such  objects,  as  additional 
sources  whence  felicities  are  to  be  multiplied.  And 
the  supposition  is  not  unreasonable  ; for  the  govern- 
ment of  the  universe  is  conducted  by  means  most 
wisely  adapted  to  their  ends,  and  as  every  thing  with 
the  Almighty  is  infinite,  there  can  be  no  assignable 
limits  to  the  number  of  these.  Objects  of  which  we 
can  now  have  no  conception,  and  new  senses  to  per- 
ceive them,  may  therefore  be  reserved  for  a more  ex- 
alted stage  of  existence.  We  know  that  here  the 
sum  of  happiness  we  are  capable  of  attaining,  de- 
pends materially  on  the  number  and  perfection  of 
our  senses,  and  among  these,  those  belonging  to  the 
soul,  by  which  we  perceive  harmony  and  beauty,  are 


INTRODUCTION. 


xxii 

of  primary  consequence  : But  in  some  individuals 
these  senses  shew  but  the  glimmerings  of  existence, 
although  capable  of  being  elicited,  cultivated  and  re- 
fined, till  they  have  power  to  transport  almost  be- 
yond the  enjoyments  allotted  to  this  infant  state  of 
being.  And  thus  by  education  may  the  human  soul  be 
improved  in  its  capacity  for  happiness  here,  in  a man- 
ner resembling  that  by  which  it  is  prepared  for  the 
higher  regions  of  bliss.  Need  I draw  the  inference 
in  favor  of  the  improvement,  in  the  present  system  of 
education,  which  it  is  the  purpose  of  this  treatise  to 
recommend  ? Does  it  not  resemble  the  creation  of 
a new  sense,  by  which  man  mounts  one  step  higher  in 
his  approaches  to  the  rank  of  superior  intelligences  ? 

And  let  not  the  gentle  sex  startle  at  the  sound 
of  Mathematics,  and  suffer  it  to  frighten  away  what- 
ever impressions  may  have  been  received  by  them  fa- 
vorable to  this  elegant  Art.  Although  it  would  be 
disgraceful  for  the  graduate  of  a college  to  be  unac- 
quainted with  the  mathematical  foundation  on  which 
his  knowledge  is  built,  the  profound  ploddings  neces- 
sary for  him  are  not  required  of  the  female  learner.— 
Her  quick  intuitive  apprehensions  may  well  dispense 
with  such  a prop. 

A little  practice  after  the  examples  that  will  be  giv- 
en, will  initiate  her  into  the  mysteries  of  the  art ; 
and  her  natural  ingenuity  and  taste  will  enable  her, 
with  the  assistance  of  a few  lessons  from  a drawing 
master,  and  the  artificial  helps  that  will  be  recom- 
mended, to  prosecute  it  to  any  height  of  perfection 
she  may  wish  to  attain. 

“ To  train  the  foliage  o’er  the  snowy  lawn,  to 
guide  the  pencil,”  and  by  its  magic  to  call  up  the  ap- 


INTRODUCTION.  xxiii 

paritions  of  cottages,  cascades,  hills  and  dales,  green 
woods  and  flowery  fields,  meandering  brooks  and 
waving  trees,  and  all  the  witcheries  of  a fairy  land  ; to 
play  with  the  children  of  FANCY ; to  arrest  the 
lovely,  fugitive,  flitting,  visionary  BEAUTIES,  and 
fix  them  with  the  permanency  which  the  enchant- 
ments of  this  art  only  can  impress,  well  becomes  the 
delicate  taste,  the  lily  hand  and  fingers  of  the  fair. 

And,  if  in  such  employments  and  in  the  contem- 
plation of  such  objects,  their  gentle  spirits  rise  in  as- 
pirations to  that  wonderful  POWER,  from  whom  all 
things  have  emanated,  the  all  beneficent  Provider 
of  such  ineffable  delights,  they  will  feel  themselves^ 
elevated  to  a region  of  pure  intellectual  enjoyments, 
far  above  that  in  which  the  untutored  and  less  favor- 
ed part  of  their  species  are  doomed  to  waste  their  ex- 
istence. 


NOTES, 

Referred  to  in  the  preceding  Introduction; 


NOTE  A — (Seepage  \ l.) 

The  following  observations  are  from  an  author 
well  known  and  justly  held  in  high  esteem  for  his 
ingenious  and  scientific  works : 

“ I need  not  observe  how  requisite  it  is  for  Paint- 
“ ers  who  put  groupes  of  figures  together,  but  also 
“ for  those  who  draw  landscapes,  or  figures  of  ma- 
“ chines  and  engines  for  books,  to  know  the  rules  of 
“ perspective.  The  want  of  this  branch  of  know- 
“ ledge  is  the  reason  why  we  see  not  only  very  bad 
cc  and  distorted  figures  of  machines  and  engines 
“ in  printed  books,  but  also  why  we  see  many  histo- 
“ rical  paintings,  in  which  the  different  figures  of 
“ men,  women,  hills,  houses,  birds  and  beasts  are  put 
“ together  without  any  regard  to  what  painters  call 
“keeping;  which  is  the  same  thing  as  representing 
“ objects  in  the  same  manner  that  they  appear  to  the 
“ eye  at  different  distances  from  it. 

“ I shall  only  mention  two  instances  in  the  w ork 
“ of  one  of  the  greatest  painters  that  ever  existed ; I 
“ mean  the  celebrated  Raphael  Urbin. 

“ Every  man  is  sensible,  that,  if  he  should  stand  by 
“ the  sea-side,  and  look  at  a boat  with  men  in  it  at 
“ some  distance,  he  could  not  distinctly  see  the  fea- 
“ tures  of  those  men,  much  less  the  wrinkles  and 
“ marks  of  the  muscles  in  their  faces  or  bare  arms. 


NOTES. 


xxv 


And  if  he  were  in  a boat  at  some  distance  from 
“ the  land,  he  could  not  perceive  the  eyes  and  beaks 
€<  of  fowls  on  the  shore. 

M Yet  so  it  is,  that  in  one  of  the  famous  Cartoons 
c<  of  Raphael,  representing  the  miraculous  draught 
“ of  fishes,  the  men  in  each  of  the  two  boats  appear 
“ of  full  size,  the  features  of  their  faces  strongly 
“ marked ; and  the  boats  are  represented  so  small, 
“ and  the  men  so  big,  that  any  one  of  them  appears 
u sufficient  to  sink  either  of  the  boats  by  his  own  bare 
“ weight ; and  the  fowls  on  the  shore  are  likewise 
“ drawn  so  big  as  to  seem  very  near  the  eye  of  the 
“ observer,  who  could  not  possibly  in  that  case  dkn 
“ tinguish  the  features  of  the  men  in  the  distant  boats ; 
“ or  supposing  the  observer  to  be  in  either  of  the 
“ boats,  he  could  not  see  the  eyes  or  beaks  of  the 
“ fowls  on  shore. 

“ The  other  instance  is  a very  capital  mistake 
“ in  Raphael’s  historical  picture  of  our  Saviour’s 
<(  Transfiguration  on  the  Mount ; where  he  is  re- 
“ presented  with  those  who  were  there  with  him,  ab 
“ most  as  large  as  the  rest  of  his  disciples  at  the  foot 
“ of  the  Mount,  with  the  father  and  mother  of  the 
“ boy  whom  they  brought  to  be  cured,  and  the  mo- 
“ ther,  though  on  her  knees,  is  more  than  half  as  tall 
a as  the  Mount  is  high.  So  that  the  Mount  appears 
“ only  of  the  size  of  a little  hay-rick,  with  a few  peo- 
“ pie  on  its  top,  and  a great  multitude  at  its  bottom 
“ on  the  ground,  in  which  case  a spectator  at  a little 
“ distance,  could  as  well  distinguish  the  features  of 
“ those  on  the  top  as  those  on  the  ground.  But  upon 
“ any  large  eminence^  deserving  the  name  of  a Mount, 
c<  that  would  be  quite  impossible.  My  only  reason 

4 


XXVI 


NOTES. 


“ for  mentioning  these  extraordinary  particulars,  is 
“ to  shew  how  necessary  it  is  for  painters  to  be  well 
“ acquainted  with  the  Rules  of  Perspective.” 

FERGUSON. 


NOTE  B. — ( see  page  14.) 

Doubtful  whether  my  meaning,  in  what  I have 
said  about  the  sound  of  language , will  be  fully  com- 
prehended, I am  tempted  to  make  a few  critical  re- 
marks to  explain  it ; and  to  this  I am  the  more  readi- 
ly induced  by  the  consideration  that  it  may  be  of 
some  use,  in  other  respects,  to  the  student,  for  whose 
hands  this  work  is  principally  intended.  For  this 
purpose*  I shall  take  an  ordinary  passage  from  Virgil, 
where,  in  enumerating  the  objects  of  the  husband- 
man's care,  he  has  occasion  to  mention  the  class  of 
vegetables,  distinguished  by  the  name  of pulse , called 
by  Botanists,  the  pod-bearing  or  leguminous  plants. 
This  he  does  in  such  a manner  that  the  expression  is 
in  itself  musical,  or  agreeable  to  the  ear ; that  it  re- 
sembles in  its  sound  what  is  intended  to  be  express- 
ed,  and,  that  it  excites  other  pleasing  ideas.  The 
passage  to  which  I allude  is  this  : 

Latum  quassante  siliqua  legumen.  Which  I would 
translate, 

The  leguminous  plant  pleased  with  the  rattling  of  its 
pod. 

Whether  this,  in  the  original,  is  not  musical,  can  be 
determined  only  by  an  appeal  to  the  ear  ; and,  un- 
less I am  much  mistaken,  there  is  something  in  quas - 
sante.  siliqua  resembling  that  soft  sound  which  is 


NOTES. 


xxv  ii 


heard  from  pods,  ripe  for  gathering,  shaken  by  the 
wind.  To  me  it  seems  not  inferior,  in  this  respect,  to 
Homer’s  y***r  of  Apollo’s  bow,  his 

of  the  terrified  Pluto,  or  his  *?*****  nctx'evB*  x*< 
the  horses  of  .Eneas;  and  in  sweetness  of  tone,  if  not  fe- 
licity of  expression,  equal  to  his  &*h  V*£V  v *******  of 
Andromache.  Besides,  one  can  hardly  read  this  line 
without  having  raised  in  his  mind  one  of  the  most 
agreeable  sights  in  nature,  a child  happy  in  the  pos- 
session of  a toy,  or  a mother  amused  with  the  sports 
of  her  children. 

It  is  in  exciting  pleasing  ideas  to  associate  with* 
those  primarily  intended  to  be  communicated,  that 
the  chief  art  of  poetry  consists.  Here  the  poet  gives 
perception  and  affection,  properties  of  animated  be- 
ings, to  the  vegetable,  and  thus  furnishes  a handsome 
specimen  of  the  prosopopeia. 

Davidson’s  translation  is, 

A joyful  crop  of  pulse  rvilh  rattling  pods. 

Now,  to  my  ears  and  to  my  understanding,  this  is 
far  from  being  a true  representative  of  the  original. 
And  thus  it  is  that  the  classics  are  ordinarily  taught. 
Their  melody  is  personated  by  discord.  The  delight- 
ful associated  and  secondary  ideas,  that  croud  about 
their  principals,  are  totally  lost  ; and  a body  the 
most  beautiful,  and  full  of  soul  and  animation,  such 
as  a Georgic  or  an  Enead,  is  exhibited  as  a mass 
destitute  of  every  attractive  quality,  excepting  per- 
haps so  much  of  the  ingenuity  of  the  original  as  can- 
not be  disguised,  or  the  interesting  matter  of  the  sto- 
ries it  relates. 

To  mistake  the  obvious  meaning  of  an  author,  is 
unpardonable  in  a translator ; not  to  do  justice  to  his 


NOTES. 


xxviii 

style  may  be  excusable ; for  the  fact  is,  that  no  man's, 
style  can  partake  fully  of  the  melody  of  language, 
unless  he  has  an  ear  that  can  detect  the  slightest 
touches  of  discord  in  a sentence,  and  a taste  that  will 
direct  him  to  the  true  medium  between  a tedious  mo- 
notony and  too  excessive  a variety  of  measure,  whe- 
ther prose  or  poetry  be  the  manner  of  his  writing. 

These  discriminating  faculties  in  regard  to  the  me- 
lody of  language,  are  what  I have  supposed  may  be 
favorably  affected  by  that  taste  for  the  kindred  har- 
monies, which  the  study  of  perspective  and  the  prac- 
tice of  drawing  are  calculated  more  immediately 
to  improve. 

When  I read  Horace,  Virgil  or  Homer,  I see,  with- 
out an  interposed  veil  of  obscure  diction,  the  most 
beautiful  images  moving  to  the  most  melodious  mu- 
sic. The  sound  of  Cicero’s  language,  little  less  than 
the  matter  it  conveys,  is  an  instrument  of  delight,  and 
both  combined  have  produced  that  wonderful  effect 
in  which  subsequent  ages  have  in  vain  attempted  to 
rival  him.  These  writers  never  insulted  their  cotem- 
poraries by  offering  for  their  admiration,  the  uncouth 
dialects  and  barbarous  phrases  current  in  the  days  of 
Theseus  and  Romulus.  The  polished  Grecians  and 
Romans  were  not  to  be  duped  by  such  literary  cun- 
ning ; they  did  not  complain  that  their  language  was 
enervated  by  a departure  from  the  rough  jargon  of 
their  ancestors,  or  poisoned  by  borrowing  sweetness 
from  neighboring  nations ; although  there  might  have 
been  some  then,  as  there  are  critics  now,  disposed  to 
plead  for  a recurrence  to  the  days  of  VORE. 


NOTES. 


xxrx 


NOTE  C— (Seepage  19.J 
As  coincident  with  several  of  the  sentiments  ad- 
vanced in  this  treatise,  the  following  passage  is  trans- 
cribed from  the  works  of  one  of  the  most  eminent 
and  most  amiable  of  moral  philosophers  : — 

“ It  is  strange  to  observe  the  callousness  of  some 
“ men,  before  whom  all  the  glories  of  Heaven  and 
“ earth  pass  in  daily  succession,  without  touching 
“ their  hearts,  elevating  their  fancy,  or  leaving  any 
“ durable  remembrance.  Even  of  those  who  pie- 
‘‘  tend  to  sensibility,  how  many  are  there  to  whom 
the  lustre  of  the  rising  or  setting  sun ; the  sparkling 
concave  of  the  midnight  sky  ; the  mountain-forest 
“ tossing  and  roaring  to  the  storm,  or  warbling  with 
■c  all  the  melody  of  a summer-evening  ; the  sweet  in- 
“ terchange  of  hill  and  dale,  shade  and  sunshine, 
“ grove,  lawn,  and  water,  which  an  extensive  land- 
“ scape  offers  to  the  view  ; the  scenery  of  the  ocean, 
“ so  lovely,  so  majestic,  and  so  tremendous  ; and 
“ the  many  pleasing  varieties  of  the  animal  and  ve- 
“ getable  kingdom,  could  never  afford  so  much  real 
“ satisfaction,  as  the  steams  and  noise  of  a ball-room, 
“ the  insipid  fiddling  and  squeaking  of  an  opera,  or 
“ the  vexations  and  wranglings  of  a card-table.” 

“ But  some  minds  there  are  of  a different  make ; 
“ who,  even  in  the  early  part  of  life,  receive  from 
“ the  contemplation  of  nature  a species  of  delight 
“ which  they  would  hardly  exchange  for  any  other. 
“ Such  minds  have  always  in  them  the  seeds  of  true 
“ taste,  and  frequently  of  imitative  genius.  At  least, 
“ though  their  enthusiastic  or  visionary  turn  of  mind 
“ (as  the  man  of  the  world  would  call  it)  should  not 
“ always  incline  them  to  practice  poetry  or  painting, 


XXX 


NOTES. 


“ we  need  not  scruple  to  affirm,  that  without  some 
“ portion  of  this  enthusiasm,  no  person  ever  became 
“ a true  poet  or  painter.  For  he  who  would  imitate 
“ the  works  of  nature,  must  first  accurately  observe 
“ them  ; and  accurate  observation  is  to  be  expected 
“ from  those  only  who  take  great  pleasure  in  it. 

“ Toa  mind  thus  disposed,  no  part  of  creation  is 
“ indifferent.  In  the  crouded  city  and  howling  wil- 
“ derness  ; in  the  cultivated  province  and  solitary 
“ isle  ; in  the  flowery  lawn,  and  craggy  mountain  ; 
“ in  the  murmuring  of  the  rivulet,  and  uproar  of  the 
“ ocean  ; in  the  radiance  of  summer,  and  gloom  of 
<c  winter ; in  the  thunder  of  Heaven,  and  in  the  whis- 
“ per  of  the  breeze  ; he  still  finds  something  to  rouse 
“ or  sooth  his  imagination,  to  draw  forth  his  affec- 
“ tions,  or  to  employ  his  understanding. 

“This  happy  sensibility  to  the  beauties  of  nature 
“ should  be  cherished  in  young  persons.  It  engages 
“ them  to  contemplate  the  creator  in  his  wonderful 
“ works  ; it  purifies  and  harmonises  the  soul,  and  pre- 
, “ pares  it  for  moral  and  intellectual  discipline  ; it 
“ supplies  a never  failing  source  of  amusement  ; it 
contributes  even  to  bodily  health  ; and,  as  a strict 
“ analogy  subsists  between  material  and  moral  beau- 
“ ty,  it  leads  the  heart  by  an  easy  transition  from  the 
“ one  to  the  other  ; and  thus  recommends  virtue  for 
“ its  transcendant  loveliness,  and  makes  vice  appear 
“ the  object  of  contempt  and  abomination.  An  in- 
timate  acquaintance  with  the  best  descriptive  poets, 
“ Spencer,  Milton  and  Thompson,  but  above  all  with 
<£  the  divine  Georgic,  joined  to  some  practice  in  the 
“ art  of  drawing,  will  promote  this  amiable  sensibili- 


NOTES.  xxxi 

“ ty  in  early  years ; for  then  the  face  of  nature  has 
“ novelty  added  to  its  other  charms,  the  passions  are 
“ not  pre-engaged,  the  heart  is  free  from  care,  and 
rt  the  imagination  warm  and  romantic.” 

BEATTIE. 


!T<\i 


- • • J . ' 1 '!  : > n . . •' 

" ‘ ■ i A j If  fM  j|  { j ,)  .j.  » 

: : > r.  • ■ L i . ) J.i  J. 

. 


* 

irriAaa 


■ 

‘ 

. 


r 

•- 

■ 

• 

. 


ELEMENTS 


OF 


PERSPECTIVE. 


DEFINITIONS. 

Perspective  is  the  art  of  finding  on  a plane,  * 

placed  between  the  eye  and  an  object,  the  several 
points  through  which  straight  lines,  drawn  from  any 
given  points  in  the  object  to  the  eye,  will  pass;  for  the 
purpose  of  making  a representation  of  such  object  on 
such  plane ; the  position  of  the  eye,  the  plane,  and 
object,  being  given. 

The  plane  on  which  objects  are  so  to  be  represent- 
ed extended  indefinitely  each  way,  is  called  the  Plane 
of  the  Picture ; and  is  generally  placed  perpendicu- 
lar (or  at  right  angles)  to  the  horizon. 

That  point  in  the  plane  of  the  picture,  to  which 
the  eye  is  supposed  to  be  perpendicular,  is  called  the 
point  of  sight. 

A line  drawn  on  the  plane  of  the  picture,  through 
the  point  of  sight  parallel  to  the  horizon,  is  called 
the  horizon  line . 

A point  in  the  horizon  line  at  a distance  from  the 
point  of  sight,  equal  to  the  distance  between  the  sup- 
posed place  of  the  eye  and  the  plane  of  the  picture, 
is  called  the  point  of  distance . 

5 


34 


ELEMENTS  of 


A horizontal  plane  intersecting  the  plane  of  the 
picture  at  any  distance  below  the  horizon  line  on 
which  the  objects  to  be  drawn  are  first  to  be  Ortho- 
graphically  projected,  is  called  the  j undam  enlal  plane. 

The  line  of  intersection  between  the  plane  of  the 
pict  ure  and  the  fundamental  plane,  is  called  the  Fun- 
damental or  Base  line. 

If,  from  any  number  of  points  in  an  object,  straight 
lines  be  drawn  perpendicular  to  the  fundamental 
plane,  such  points  are  said  to  be  orthographically 
projected  on  the  plane,  where  it  is  met  by  such  per- 
pendiculars. 

The  heighth  to  which  the  perspective  representa- 
tion of  an  object  is  raised  above  the  base  line  in  the 
plane  of  the  picture,  is  called  the  perspective  elevation . 

The  perspective  representation  of  the  heighth  of  an 
object  above  the  fundamental  plane,  is  called  theper- 
spective  altitude. 

The  angle,  by  which  any  straight  line  deviates  from 
a vertical  plane  supposed  to  be  placed  at  right  an- 
gles to  the  plane  of  the  picture,  is  called  the  angle  of 
inclination. 

The  angle  by  which  any  straight  line  deviates  from 
a horizontal  plane,  is  called  the  angle  of  declination. 
PROPOSITION  1st  .—Fig.  1. 

If,  from  any  given  point  in  an  object,  a straight 
line  be  drawn  at  right  angles  to  the  plane  of  the  pic- 
ture till  it  meets  it,  and  from  thence  another  straight 
line  be  drawn  on  the  plane  of  the  picture  to  the  point 
of  sight,  the  given  point  will  then  be  represented  some 
where  in  this  line. 

DEMONSTRATION. 

Let  GH  be  the  plane  of  the  picture,  E the  point 


PERSPECTIVE. 


35 


of  sight,  F the  given  point  in  the  object,  FI  the  line 
drawn  from  it,  at  right  angles  to  the  plane  of  the  pic- 
ture, meeting  it  in  I ; and  IE  the  line  drawn  thence  to 
the  point  of  sight.  Continue  FI  to  C & D,  through  E 
draw  AB  parallel  to  CD  ; also  draw  AC  and  BD ; 
then  ABCD  will  be  a plane  intersecting  the  plane  of 
the  picture  in  the  line  IE.  Suppose  B the  place  of 
the  eye,  and  FB  a straight  line  drawn  from  the  given 
point  to  the  eye.  It  is  evident  that  the  line  FB 
will  be  in  the  plane  ABCD,  and  therefore  will  inter- 
, - 'A  sect  the  plane  of  the  picture  somewhere  in  the  line 
IE.  Q.  E.  D. 

PROPOSITION  2d. — Fig.  2. 

If  EB  be  the  line  drawn  by  Proposition  1st.  some- 
where in  which  the  given  point  in  the  object  will  be 
represented,  B being  the  point  of  sight,  A the  point 
of  distance,  and  EG  parallel  to  AB.  Then  if  EH 
laid  off  in  a direction  contrary  to  that  from  B to  A 
be  equal  to  the  distance  of  the  object  from  the  plane 
of  the  picture  ; and  AH  be  drawn  : the  point  C where 
it  intersects  the  first  mentioned  line,  will  represent 
the  given  point,  or  CL  will  represent, its  perspective 
elevation. 

DEMONSTRATION. 

Let  BF  be  the  profile  of  the  plane  of  the  picture, 
G the  given  point,  and  a straight  line  be  draw  n from 
it  to  the  eye  at  A ; it  is  evident  that  DF,  (the  dist- 
ance between  the  place  where  it  intersects  the  plane 
of  the  picture  and  the  line  EG,)  will  be  its  elevation; 
and  this  line  DF  is  equal  to  CL,  or  CD  is  parallel  to 
EG ; for  if  it  be  not,  make  Cl  parallel  to  EG,  and 
through  I draw  AK.  Then,  from  the  properties  of 
similar  triangles  it  will  be ; 


36 


ELEMENTS  OF 


In  the  Triangles  ACI,AHK ; Cl:  HK : : AI : AK  ) W 
In  the  Triangles  ABI,KFI ; AI : AK : : BI : BF  > ^ 
In  the  Triangles  BIC,BFE ; BI : BF  : : Cl  : EF  ) p 
Therefore, 

Cl  : HK  : : Cl  : EF.  (E.  11,  5.) 

And  Therefore, 

HK-EF.  (E.  9,  5.) 

But  HG  is  equal  to  EF,  for  EH  was  made  equal 
to  FG,  wherefore  HK  is  not  equal  to  EF,  neither, 
therefore,  is  Cl  parallel  to  EJG.  In  the  same  manner 
it  may  be  demonstrated  that  no  other  line  drawn  from 
C to  BF,  but  CD  is  parallel  to  EG,  wherefore  CD  is 
parallel  to  EG,  and  of  consequence  CL  is  equal  to 
DF,  the  perspective  elevation  of  the  given  point. 
Q.E.D. 

PROPOSITION  3d. — Fig.  3. 

If  K on  the  plane  of  the  picture  be  the  perspective 
representation  of  a given  point  on  the  fundamental 
plane,  and  it  be  required  to  represent  another  given 
point  above  it  of  the  lieighth  EF,  take  any  point  in 
the  horizon  line  as  A,  draw  AE,  and  AF ; through  K 
draw  KG  parallel  to  the  horizon  line,  till  it  meet 
AF  in  G,  and  from  G draw  the  perpendicular  line 
GC,  till  it  meet  AE,  make  MK  equal  and  parallel  to 
GC ; M will  then  represent  the  other  given  point,  and 
MK  will  be  its  perspective  altitude. 

DEMONSTRATION. 

Let  LI  be  the  profile  of  the  plane  of  the  Picture, 
F a point  in  the  fundamental  plane,  E another  point 
above  it,  and  B the  place  of  the  eye ; complete  the 
figure  by  drawing  the  lines  BF,  and  BE,  PI  and  K 
being  of  equal  elevation.  It  is  evident  that  D and 
H,  where  these  lines  intersect  the  plane  of  the  pic- 


PERSPECTIVE. 


£/f-  c 


37 

ture,  will  be  the  perspective  elevations  respectively 
of  E and  F,  or  DH  will  be  the  perpendicular  dis- 
tance between  the  points  on  the  plane  of  the  picture 
representing  E and  F.  But,  CG  is  equal  to  DH, 
for,  from  the  properties  of  equiangular  Triangles,  it 
will  be : 

In  the  Triangles  AEF,ACG;  FE : GC : : FA : GA  ) t*j 
In  the  Triangles  FAB, FGH;  FA : GA: : FB  : HB  > 
IritheTrianglesBEF,BDH ; FB  : HB  : : FE  :HD ) P 
Therefore, 

FE  : GC : : FE  : HD.  (E.  11.  5.) 

Wherefore, 

GC=HD.  E.  9.  5. 

But  MK  was  made  equal  to  GC,  therefore  MK 
will  also  be  equal  to  HD,  which  is  the  perspective 
altitude  of  the  point  E.  Q,.  E.  D. 

These  propositions  furnish  rules  by  which  all  ob- 
jects may  be  represented  perspectively  ; and  in  their 
application  to  practice,  observe  the  following 

GENERAL  DIRECTIONS. 

On  the  fundamental  plane  project  orthographi- 
cally  all  the  points  in  the  object  to  be  represented 
that  may  be  considered  necessary  for  delineating  its 
outlines:  From  these  points,  (by  proposition  1st) 
draw  straight  lines  perpendicular  to  the  fundamental 
or  base  line,  and  from  the  points  where  they  intersect 
it  draw  straight  lines  to  the  point  of  sight;  in  these 
lines,  (by  proposition  2d)  find  the  Perspective  eleva- 
tion of  the  several  points  to  be  represented,  then  (by 
proposition  3d)  drawr  the  perspective  altitudes  of  the 
several  points  according  to  their  respective  heights ; 
and  finally  connect  the  several  points  in  the  repre- 
sentation, as  they  are  in  the  outlines  of  the  objects. 


38 


ELEMENTS  OF 


Besides  these,  some  auxiliary  rules  may  be  deduc- 
ed from  the  same  principles,  as  the  following  propo- 
sitions will  indicate. 

PROPOSITION  4th. 

If  a line  on  the  fundamental  plane  be  neither  at 
right  angles,  nor  parallel,  to  the  pfcwe  of  the  picture 
or  base  line,  and  that  line  be  continued  to  the  plane 
of  the  picture  or  base  line,  and  a line  be  drawn 
thence,  on  the  plane  of  the  picture,  to  a point  in  the 
horizon  line,  distant  from  the  point  of  sight  by  the 
tangent  of  the  angle  of  inclination,  (the  distance  of 
the  eye  from  the  plane  of  the  picture  being  radius) 
then  will  the  first  mentioned  line  be  represented  in 
the  line  so  drawn  on  the  plane  of  the  picture. 
DEMONSTRATION.— Fig.  1. 

Suppose  FI  and  BE  not  at  right  angles  to  the 
plane  of  the  picture  GH,  then  draw  BK  at  right  an- 
gles to  the  plane  of  the  picture  ; K will  then  be  the 
point  of  sight,  and  E may  be  called  a casual  point  of 
sight,  whose  distance  EK  from  the  point  of  sight  will 
be  the  tangent  (to  the  radius  BK)  of  the  angle  of  in- 
clination KBE,  and  (by  proposition  1st)  FI  is  repre- 
sented in  the  line  EL  ft.  E.  D, 

For  the  same  reason,  lines  in  objects  declining  up- 
wards or  downwards  from  a horizontal  plane,  will 
have  their  casual  points  of  sight  below  or  above  the 
horizon  line  by  the  tangent  of  the  angle  of  declina- 
tion, to  the  same  radius,  if  there  be  no  horizontal  in- 
clination ; otherwise  to  a radius  which  shall  be  the  se- 
cant of  the  angle  of  such  inclination : For  EL  is  the 
tangent  of  the  angle  of  declination  EBL  to  the  radius 
BE  which  is  the  secant  of  the  angle  of  inclination 
EBK.  If  the  inclination  be  to  the  right,  the  casual 


PERSPECTIVE. 


39 


point  must  be  laid  off  to  the  left  of  the  point  of  sight  ; 
if  the  declination  be  upwards,  the  casual  point  must 
be  laid  downwards  from  the  horizon  line,  and  vice 
versa . 

The  casual  point  may  be  found  in  the  following 
manner : (Fig.  4th.)  S 

If  HO  be  the  horizon  line,  BA  the  base  line,  S the 
point  of  sight,  D the  point  of  distance,  and  IKLM  a 
parallelogram  on  the  fundamental  plane  to  be  drawn 
perspectively.  Continue  LK  and  LM  to  U and  F ; 
draw  LY  at  right  angles  to  the  base  line  and  equal 
to  SD ; through  Y draw  EG  parallel  to  the  base 
line  till  it  meet  LU  and  LF  in  E and  G ; make  GS  % 
equal  to  GY,  and  SP  to  EY ; then  will  C be  the 
casual  point  for  LM  and  all  lines  parallel  to  it ; for, 
CS,  or  GY  which  wras  made  equal  to  it,  is  the  tan- 
gent of  the  angle  of  inclination  YLG  of  the  line  LM, 
to  the  radius  LY,  which  is  equal  to  SD  the  distance 
between  the  eye  and  the  plane  of  the  picture.  For 
the  same  reason  P is  the  casual  point  for  LK,  and  all 
lines  parallel  to  it : Wherefore,  CF,  CX,  PU  and 
PW  being  drawn,  their  points  of  intersection,  i.LLm. 
will  be  the  perspective  of  I.K.L.M. 

Suppose  now  that  the  end  IK  of  the  parallelogram 
be  raised  above  the  fundamental  plane  to  the  height 
qa>  then  through  a draw  LT,  making  ET  at  right 
angles  to  LU,  and  from  P lay  off  P p at  right  angles 
to  HO  and  equal  to  ET ; p will  then  be  the  casual 
point  for  LK  and  MI  raised  as  aforesaid:  For  P 'p% 
which  is  equal  to  ET,  is  the  tangent  of  the  angle  of 
declination  ELT  to  the  radius  EL,  which  is  the  se- 
cant of  the  angle  of  inclination  ELY,  and  in  this  case 
the  perspective  of  KL  and  IM  will  be  in  the  line 
drawn  from  p through  l and  in. 


40 


ELEMENTS  OF 


Since  aq  is  supposed  the  perpendicular  drawn  to 
the  fundamental  plane  from  K elevated  to  a,  the 
point  q will  be  the  orthographic  projection  of  K so 
elevated,  and  qt  of  the  line  IK ; qt  continued  will 
strike  the  base  line  at  b,  and  IK,  so  elevated,  conti- 
nued, will  strike  above  it  a distance  equal  to  qa  to 
wit,  at  vy  wherefore  K and  I will  then  be  found  in  a 
line  drawn  from  V to  the  casual  point  C,  to  w it,  at  tv 
and  s,  where  it  is  intersected  by  pm  and  ps ; lm,rvs 
w7ill  then  be  the  perspective  of  IM,LK,  so  elevated. 

If  IK  remaining  on  the  fundamental  plane ; ML 
had  been  elevated  to  the  height  aq,  then  would  c in- 
stead of  p have  been  the  casual  point  of  si^ht  for  IM 
and  KL. 

If  the  perpendicular  S D be  made  equal  to  SD=* 
LY  and  lines  be  drawn  from  D parallel  to  LK  and 
LM,  they  will  intersect  HO  in  C and  P because  the 
triangles  ELY  and  YLG  are  similar  and  equal  to 
PjDS  and  SZ)C ; the  casual  points  C and  P may 
therefore  be  found  in  this  as  the  easiest  manner. — 
Now  if  a line  be  drawrn  from  L to  D , intersecting  EG 
in  8 and  HO  in  7,  S 7 will  be  equal  to  Y 8,  and,  as 
before  shew  n,  a distance  equal  to  Y 8,  laid  off  from 
S on  HO  will  give  the  casual  point  for  the  line  L 8 ; 
wherefore  7 will  be  the  casual  point  for  L 8,  and  L 8 
continued  to  the  base  line  and  thence  to  7 will  be  re- 
presented in  such  continuation  ; whence  it  follows, 
that  w here  a straight  line  drawn  from  L to  D inter- 
sects either  UP  or  FC,  (in  which  LK  and  LM  are  re- 
presented) to  wit  at  Z,  will  be  the  perspective  repre- 
sentation of  L.  In  the  same  manner  lines  drawn 
from  M,  I and  K,  to  J3  will,  at  their  intersections  with 
CF,  CX,  PYV  and  PLT  give  the  points  representing 
M,  I and  K. 


PERSPECTIVE. 


41 


Henfce  we  have  still  an  easier  method  of  drawing 
the  perspectives  of  lines  inclined  to  the  plane  of  the 
picture,  thus  : If  it  be  required  to  draw  the  perspec- 
tive of  9,  10,  continue  that  line  to  the  base  line  at  1 1, 
from  D draw  DC , parallel  to  it ; draw  1 1 C,  D 10  and 
D 9 and  the  points  of  intersection  if,  12  and  13  will 
represent  10  and  9.  ^ 

Thus  also,  by  making  PZ>^ equal  to  ELT,  or  the 
angle  of  declination,  and  drawing  P 14  at  right  an- 
gles to  P D and  making  P p and  Pc  equal  to  P 14  may 
p and  c be  found,  or  the  casual  points  of  LK  and 
MI  declining  upwards  or  downwards  as  aforesaid. 

From  this  proposition,  and  from  proposition  1,  it 
follows,  that  all  lines  parallel  to  each  other,  and  not 
parallel  to  the  plane  of  the  picture,  will  be  repre- 
sented in  lines  meeting  in  one  point,  those  which  are 
at  right  angles  to  the  plane  of  the  picture  will  be  re- 
presented in  lines  meeting  in  the  point  of  sight ; and 
those  which  are  inclined  to  the  plane  of  the  picture, 
will  be  represented  in  lines  meeting  in  some  casual 
point. 

PROPOSITION  5th. 

All  lines  parallel  to  the  plane  of  the  picture,  and 
equi-distant  from  it,  will  be  represented  by  lines 
parallel  to  them,  and  having  the  same  proportions  to 
each  other  ; and  hence  any  figures  whose  parts  are 
equi-distant  from  the  plane  of  the  picture  will  be  re- 
represented by  similar  figures  ; that  is,  squares  will 
be  represented  by  squares,  circles  by  circles,  &c.  &c. 
DEMONSTRATION. — Fig.  5. 

Let  AB  be  a section  of  the  plane  of  the  picture, 
C the  eye,  DE  and  FG  two  lines  parallel  to  AB,  and 

equi-distant  from  it ; and  HI  and  KL  the  lines  re- 

6 


42 


ELEMENTS  OF 


spectively  representing  them.  Then  will  HI  be  to 
KL  as  HE  is  to  FG.  Join  E,F;  DG  will  then  be 
one  line  parallel  to  AB.  Then  from  the  properties 
of  similar  triangles,  it  will  be, 

In  Triangles  CGD,CLH ; CG : CL : : DG : HL  \ H 
In  Triangles  CGE,CLI;CG:  CL  r.EG  .lL  ] & 
Therefore  DG  :HL. : EG  : IL  (El  1,5) 
and  DG : HL : : DE : HI(E  1 9,5) 
and  for  the  same  reason  DG : HL : : FG  : KL 

Wherefore  DE : FG : : HI  :KL(El  1,5)  £ 
PROPOSITION  6th. 

The  diagonals  of  squares  having  two  sides  parallel 
andi  two  sides  at  right  angles  to  the  plane  of  the  pic- 
ture, will  have  their  casual  points  of  sight  in  the  point 
of  distance  laid  off  either  way  from  the  pointof  sight 
on  the  horizon  line. 

DEMONSTRATION.— Fig.  6. 

The  diagonals  of  squares  so  situated  will  incline  to 
the  plane  of  the  picture  under  angles  of  45°,  the  tan- 
gents of  which  are  equal  to  radius,  (and  by  proposi- 
tion 4th)  the  distance  of  the  casual  points  from  the 
point  of  sight  is  equal  to  the  tangent  of  the  angle  of 
inclination  (the  distance  of  the  eye  from  the  plane  of 
the  picture  being  radius) ; wherefore,  the  casual 
point  of  sight  of  every  such  diagonal  will  be  in  the 
point  of  distance  laid  off  either  way  from  the  point 
of  sight  in  the  horizon  line.  Q.E.D. 

Hence  we  have  a convenient  substitute  for  the 
rule  deduced  from  propositions  1st  and  2d  to  find 
the  perspective  of  points  given  on  the  fundamental 
plane ; for  if  from  any  such  point  a line  be  drawn  to 
. the  right,  and  another  to  the  left,  meeting  tlte!  base 
line  under  angles  of  45°,  and  lines  be  thence  drawndo 


PERSPECTIVE. 


43 


the  casual  points  of  sight  (which  will  be  the  same  as 
for  the  diagonals  above  mentioned,  that  is  in  the 
points  of  distance)  where  the  last  mentioned  lines 
intersect  each  other  will  be  the  perspective  of  the  gi- 
ven point:  Thus, 

Figure  6. 

If  A be  the  point  of  sight,  B and  C the  points  of 
distance^  then  C and  B will  be  the  casual  points  of 
sight  for  the  diagonals  of  the  squares  DOEG  and 
EGFH,  and  also  for  all  lines  meeting  the  base  line 
JDN  under  angles  of  45°.  If,  therefore,  any  point, 
as  L,  is  to  be  drawn  perspectively,  draw  LM  and 
LN  to  fall  on  DN  under  angles  of  45°  and  draw  MB  „ 
and  NC  ; the  point  of  intersection  l will  then  be  the 
perspective  of  L. 

Figure  7, 

Shews  the  perspective  of  a cube,  the  bottom  and 
top  of  which  are  made  by  drawing  the  diagonals  as 
in  tig.  6 : thus,  make  GF  equal  to  DG  ; draw'  DB  and 
FC,  and  from  the  point  of  intersection  o drawT  to  pa- 
rallel to  DG,  and  from  e where  it  intersects  CG  drawr 
eD  ; DGo?  w ill  then  be  the  bottom  of  the  cube. — 
Having  made  the  square  DG(/g  for  the  front  side  of 
the  cube,  from  dg  draw'  the  top  in  the  same  manner 
as  the  bottom  was  drawn  from  DG,  and  connect  the 
several  corners. 

The  foregoing  propositions  shew  the  several  ways 
in  which  objects  may  be  perspectively  represented. 
The  practitioner  w ill  use  such  of  them  as  he  will  find 
most  convenient  for  his  occasion.  A few  examples 
of  those  different  methods  will  now  be  given. 

In  the  succeeding  figures  HO  will  denote  the  ho- 
rizon line  ; BA  the  base  line  ; S the  point  of  sight ; 


44 


ELEMENTS  OF 


D the  point  of  distance,  and  C and  P the  casual  points 
of  sight.  The  plaee  immediately  below  the  base 
line  is  considered  as  the  fundamental  plane,  and  the 
place  of  the  eye  to  be  on  the  opposite  side  of  the 
plane  of  the  picture. 

It  is  here  proper  to  apprise  the  reader,  that  for  the 
sake  of  adapting  the  figures  to  the  size  of  the  book, 
they  are,  in  the  following  examples,  necessarily 
made  too  small  to  serve  as  precedents,  in  point  of  size, 
for  practical  drawing,  in  which  the  point  of  distance 
from  the  point  of  sight  ought  never  to  be  less  than 
eight  inches,  that  being  the  least  distance  at  which  the 
human  eye  generally  can  distinctly  discern  objects ; 
and  the  greater  the  point  of  distance  is  taken,  and 
the  less,  in  proportion,  the  field  of  the  picture,  the 
less  will  that  distortion  appear  which  is  observed  in 
objects  represented  remotely  to  the  right  or  left  of 
the  centre  of  the  picture.  It  has  been  assumed,  by 
some  waiters  on  perspective,  as  a general  rule,  that 
the  horizontal  extent  of  the  picture  should  not  ex- 
ceed the  side  of  an  equilateral  triangle,  in  the  oppo- 
site angle  of  which  the  eye  is  supposed  to  be  placed ; 
or  that  no  object  ought  to  be  taken  into  a picture 
which  is  seen  at  a greater  distance  than  thirty  de- 
grees to  the  right  or  left  of  the  point  of  sight.  Al- 
though this,  as  it  regards  the  precise  angle,  is  an  ar- 
bitrary rule,  it  will  be  well  to  observe  it. 

It  may  not  be  amiss  to  remark  here  also,  that  to 
view  a drawing  to  the  best  advantage,  the  eye  should 
be  placed  exactly  in  that  point  where  it  was  suppos- 
ed to  be,  that  is,  in  the  point  of  distance  directly  op- 
posite to  the  point  of  sight. 


PERSPECTIVE. 


45 


EXAMPLE  1st. 

To  draw  the  shape  of  a house,  the  body  of  which 
is  a parallelapiped,  and  the  roof  a prism,  in  a posi- 
tion oblique  to  the  plane  of  picture. 

Figure  ^ 

Let  1KLM  be  the  base  of  the  figure  on  the  funda- 
mental plane,  BV  the  heighth  of  its  perpendicular 
side,  NR  the  orthographic  projection  of  the  upper 
edge  of  the  roof  or  prism,  and  BQ,  its  height. 

From  IKLM,  according  to  proposition  1st,  draw 
the  perpendiculars  la,  K6,  Lc,  Me?,  and  from  a,  b , c,  d , 
draw  straight  lines  to  the  point  of  sight  S.  Then, 
according  to  proposition  2d,  lay  off  ac , bf \ eg  and  dh , 
equal  to  la,  K£>,  L c and  Me?,  respectively,  and  from 
e,/,  g,  h,  draw  straight  lines  to  the  point  of  distance 
D ; connect  the  points  i,  k , /,  m,  where  the  lines,  so 
drawn  from  a,  b , c,  d,  and  e , /,  g , h,  intersect  each 
other ; then  will  i}  k,  l,  m be  the  perspective  of  IKLM. 
In  the  next  place,  according  to  proposition  3d,  on 
i,  k,  1,  m raise  the  perspective  altitude  of  BV,  thus  : 
take  any  point,  as  T,  in  the  horizon  line,  and  draw 
TB  and  TV  ; from  i,  k,  /,  m draw  horizontal  lines  to 
TB,  and  from  the  several  points  t,  uy  v,  wy  where  they 
intersect  it,  draw  perpendiculars  to  TV.  On  i,  ky  /,  m9 
raise  perpendiculars  respectively  equal  to  those  on 
ty  Uy  v,  Wy  and  connect  1,  2,  3,  4,  their  upper  ends,  by 
straight  lines  as  in  the  figure,  which  will  then  be  the 
upper  side  of  the  parallelapiped  as  seen  from  below, 
for  in  this  case  it  is  above  the  point  of  sight. 

To  draw  the  roof  or  prism  : from  N draw  the  per- 
pendicular Np  and  from  p draw  pS9  then  will  n,  where 
this  line  intersects  ik,  be  the  perspective  of  N ; in 
the  same  manner  find  r,  the  perspective  of  R ; draw 
TO  ; from  n and  r draw  horizontal  lines  to  BI,  and, 


46 


ELEMENTS  OF 


from  the  points  where  they  strike  it,  draw  perpendi- 
culars TO,  and  equal  to  them  make  the  perpendicu- 
lars n 5 and  r 6,  draw  1,  5 — 2,  5 — 3,  6 — 4,  6 and  5, 6, 
which  will  give  the  perspective  of  the  roof  or  prism. 
In  perspective,  all  the  parts  are  commonly  first  drawn 
as  if  the  figures  were  transparent ; but,  in  finishing, 
those  parts  only  are  drawn  which  are  not  hid  from 
the  eye  by  others,  as  ki,  im,  k2 , il,  mi,  2,  5 — 1,  5 — 
5,  6 and  6,  4. — ( See  W.) 

The  perspectives  of  two  oblique  parallel  lines  pro- 
duced will  meet  in  their  casual  point  of  sight ; which 
may  therefore  thus  be  found,  as  a substitute  for  the 
method  directed  under  proposition  4th : kl  and  im 
produced  will  meet  in  P,  to  which  2,3 — 1,4  and 
5,  6 are  also  drawn — ik  and  ml  produced  will  meet 
in  C,  to  which  1,  2 and  3,  4 are  also  drawn.  If 
then,  any  number  of  oblique  parallel  lines  are  to  be 
drawn  (as  for  example  the  boarding  of  the  side  of  a 
house)  it  is  a convenient  method,  first  to  find  their 
casual  point  of  sight  in  this  manner,  in  order  to  show 
the  direction  in  which  they  are  to  be  drawn,  as  ex- 
emplified at  W. 

EXAMPLE  2d, 

Shewing  a different  method  of  drawing  perspec* 
live  altitudes. 

Figure  9. 

Draw  the  perspective  of  IKLM,  as  in  the  preced- 
ing example,  or  according  to  the  method  described 
in  the  latter  part  of  proposition  4,  which  is  here  ex- 
emplified : — Thus, 

Make  the  perpendicular  SZ>,  equal  to  SD,  make 
DP  parallel  to  KL  and  IM  ; continue  KL  and  IM 
to  X and  W ; draw  PX  and  PW>  draw  straight  lines 


PERSPECTIVE. 


47 


also  from  D to  I,  K,L  and  M,  and  where  these  in- 
tersect PX  and  PW,  to  wit : at  i,  k , l,  m,  will  he  the 
perspective  representation  of  I,K,L,M. 

Draw  VU  and  QT  parallel  to  the  horizon  ; con- 
tinue la,  K6,  L c and  M d to  VU  ; then  will  the  se- 
veral points,  where  these  lines  intersect  VU,  be  the 
points  where  lines  at  right  angles  to  the  plan  of  the 
picture,  drawn  from  IKLM  raised  to  the  height 
V,  w ould  strike  it ; and  by  proposition  2d,  w here 
lines  drawn  thence  to  the  point  of  sight  S,  intersect 
perpendiculars  raised  on  i,  /,  k , m,  will  be  found  the 
perspective  of  IKLM  raised  as  aforesaid,  as  at  1,  2,  3, 
4.  Thus  the  perpendicular  from  K,  being  continued 
to  u,  the  line  drawn  thence  to  the  point  of  sight  S 
intersects  the  perpendicular  raised  on  A:,  at  2 ; 2 will 
therefore  be  the  perspective  of  K,  raised  to  the 
heighth  V,  and  so  with  the  rest.  Again,  because 
NR  is  to  be  raised  to  the  height  Q,  continue  N p and 
R#  to  QT,  and  from  the  points  v and  y , where  they 
strike  it,  draw  straight  lines  to  S,  intersecting  the  per- 
pendiculars raised  on  n and  r,  at  5 and  (5,  which  will 
therefore  be  the  perspectives  of  N and  R,  raised  to  the 
height  Q. 

EXAMPLE  3d. 

To  draw  perspective  altitudes  by  the  casual  points 
of  sight. 

Figure  #. 

Having  drawn  the  perspective  of  IKLM  accord- 
ing to  the  directions  under  proposition  4th,  from  U 
raise  a perpendicular  to  VZ,  and  x , the  point  where 
it  strikes  it,  will  be  the  point  where  KL,  raised  to  the 
height  V,  and  produced,  w ill  strike  the  plane  of  the 
picture;  then,  in  the  line  drawn  thence  to  the 


43 


ELEMENTS  OF 


casual  point  P,  will  be  found  the  perspective  of  KL 
so  raised,  (according  to  proposition  4th)  and  the 
points  2 and  3,  where  it  intersects  the  perpendiculars 
raised  on  k and  7,  will  be  the  perspective  of  E and  L, 
raised  as  aforesaid.  In  the  same  manner,  by  raising 
a perpendicular  from  W to  VZ,  and  drawing  a line 
thence  to  P,  intersecting  perpendiculars  raised  on  im , 
we  find  the  points  1,  4,  for  the  perspective  of  IM. — 
Instead  of  P,  the  casual  point  C might  have  been 
used,  working  from  KI  and  LM,  instead  of  KL  and 
IM.  To  find  the  perspective  of  NR,  produce  it  till  4 
it  meet  BA,  thence  draw  a perpendicular  to  y , the 
height  of  Q,,  thence  draw  yV,  and  where  it  intersects 
perpendiculars  raised  on  n,  r,  to  wit : at  5 and  6,  will 
be  the  perspective  of  NR,  raised  to  the  height  Q,. 

In  drawing  the  perspective  altitudes  of  horizontal 
parallelograms,  after  having  found  that  of  one  of  the 
corners,  the  next  may  be  found  by  the  intersection 
of  a line  drawn  thence  to  the  casual  point,  with  the 
corresponding  perpendicular  ; and  this  being  found 
the  next  is  found  in  the  same  way,  and  so  on : Thus, 
having  found  1,  a line  drawn  thence  to  C,  will  give  2 
a line  drawn  thence  to  P will  give  3,  and  a line 
drawn  from  C,  through  3,  will  give  4.  For  if  two 
lines  intersecting  each  other,  be  drawn  perspectively, 
their  point  of  intersection  will  be  represented  by  the 
point  of  intersection  in  the  perspective. 

EXAMPLE  4th. 

To  draw  the  same  by  angles  of  forty-five  degrees. 

Figure  10. 

From  K draw  KW  and  KX,  meeting  the  base  line 
under  angles  of  forty-five  degrees  ; from  W draw  a 
straight  line  to  D on  the  right ; and  from  X draw  a 


PERSPECTIVE.  49 

Straight  line  to  D on  the  left ; and  the  point  k , where 
these  two  lines  meet,  will  (by  proposition  6th)  be  the 
perspective  of  K.  In  the  same  manner  find  i,  /,  m, 
n,  r,  the  perspective  of  ILMNR  ; from  W raise  a 
perpendicular  to  Y,  making  WY  equal  to  BV,  draw 
a straight  line  from  Y,  to  D on  the  right,  and  on  k, 
raise  a perpendicular  till  it  meet  it  at  2 ; then  will  2 
be  the  perspective  of  K,  raised  to  the  height  V ; and 
proceed  in  the  same  manner  to  find  the  perspective 
altitudes  of  all  the  other  points  in  the  figure. 

In  order  to  practice  in  this  manner,  it  will  be  ne- 
cessary to  have  a thin  board,  in  the  shape  of  a right 
angled  triangle,  having  the  two  legs  exactly  equal  to 
each  other  ; then  by  laying  a ruler  parallel  to  the 
base  line  below  the  figure  to  be  drawn,  and  applying 
to  it  the  hypothenuse  of  the  triangle,  if  one  of  the 
legs  be  made  to  touch  any  of  the  points  in  the  figure* 
a line  drawn  along  that  leg  will  meet  the  base  line 
under  an  angle  of  forty-five  degrees  ; the  other  leg 
is  used  to  draw  the  contrary  way. 

In  many  sided  figures,  where  there  are  few  paral- 
lel lines,  this  is  perhaps  the  most  expeditious,  as  well 
as  the  neatest  way  of  perspective  drawing ; but  where 
there  are  many  oblique  parallel  lines,  it  will  be  easi- 
er to  draw  from  the  casual  points,  as  shewn  in  the  3d 
example  ; either  of  these  methods  however  need  not 
be  adopted,  in  complex  drawings,  to  the  exclusion  of 
others  ; but  sometimes  the  one,  and  sometimes  the 
other,  may  be  chosen  as  the  practitioner  shall  find 
best  for  his  purpose. 


7 


50 


ELEMENTS  OF 


EXAMPLE  5th. — Fig.  11. 

To  draw  Curvilinear  Figures . 

First  circumscribe  them  with  the  simplest  rectili- 
neal figures*  of  which  draw  the  perspective  ; and  in 
the  same,  draw  the  perspective  of  the  given  figure, 
as  correct  as  can  be  judged  by  the  eye.  Circles  are 
best  inscribed  in  squares,  having  their  sides  parallel 
and  perpendicular  to  the  base  line.  Thus,  if  it  be  re- 
quired to  draw  a figure  in  the  shape  of  a churn,  or 
frustum  of  a cone,  having  its  bottom  equal  to  the  cir- 
cle N,  and  its  top  equal  to  C ; round  them  circum- 
scribe the  squares  EFPG  and  IKML*  having  their 
sides  parallel  and  perpendicular  to  the  base  line. 
Continue  the  perpendicular  sides  to  the  base  line,  and 
draw  straight  lines  thence  to  the  point  of  sight;  and 
from  Q and  T,  where  the  diagonals  produced  strike 
the  base  line,  draw  straight  lines  to  the  points  of  dis- 
tance as  in  the  figure.  Then  will  the  points  of  inter- 
section c,fg,  p , be  the  perspectives  of  E,  F,  G,  P,  and 
i,  k , l,  m,  will  be  the  perspectives  of  I,  K,  L,  M,  the 
orthographic  projection  of  the  square  circumscribed 
about  the  top  of  the  frustum  to  be  drawn.  On  (1, 
and  T raise  the  perpendiculars  Q,R,  and  TV,  equal 
to  the  heighth  of  the  frustum.  From  R,  and  V,  draw 
straight  lines  to  the  points  of  distance ; and  1,  2,  3,  4, 
where  these  intersect  perpendiculars  raised  on  i,  k,  l, 
m,  will  be  the  perspective  altitudes  of  i,  k,  l,  m : Then 
in  efg  h and  1,  2,  3,  4,  draw,  for  the  perspectives  of 
the  bottom  and  top  of  the  frustum,  the  curved  figures 
touching  the  perspectives  of  the  middle  of  the  sides 
of  the  circumscribed  squares,  and  crossing  the  per- 
spectives of  the  diagonals  in  points  found  thus  ; from 
5 and  6,  where  the  circle  N intersects  the  diagonals 


PERSPECTIVE. 


51 


of  the  circumscribing  square,  draw  perpendiculars  to 
the  base  line,  and  from  the  points  7,  8,  where  they 
meet  it,  draw  lines  to  the  point  of  sight  : where  these 
lines  intersect  the  perspectives  of  the  diagonals,  the 
perspective  of  the  circle  must  cross  them.  And  last- 
ly, draw  straight  lines  for  the  sides  of  the  frustum, 
touching  the  perspectives  of  the  two  ends.  This 
shews  an  oblique  view  of  the  object,  and  gives  it 
somewhat  of  a distorted  appearance,  which  is  una- 
voidable in  groups ; but  where  a drawing  is  required 
* of  a single  object,  especially  of  cones  and  cylinders, 
it  will  be  adviseable  to  take  a front  view,  or  as  near- 
ly so  as  may  be.  The  base  of  the  frustum  in  the 
example,  will  then  assume  the  shape  represented  at 
W,  and  the  whole  figure  be  like  that  at  Y. 

X is  the  perspective  of  a cylinder  whose  sides  are 
perpendicular  to  the  plane  of  the  picture,  and  the 
ends  parallel  to  it ; in  which  case,  according  to  propo- 
sition 5th,  the  perspectives  of  the  ends  will  be  cir- 
cles, and  by  proposition  1st,  the  sides  will  appear  in 
lines  drawn  to  the  point  of  sight : Z is  the  drawing  of 
it  completed. 

EXAMPLE  6th. — Fig.  12. 

To  draw  the  perspective  of  lines  divided  into  equal 
parts — - 

If  a line  be  parallel  to  the  plane  of  the  picture,  its 
equal  divisions  will  be  represented  by  equal  divisions 
in  the  perspective.  No  particular  directions  need 
therefore  be  given  for  the  operation. 

If  a line  at  right  angles  to  the  plane  of  the  picture, 
be  divided  into  equal  parts,  as  EF  divided  at  a and  b ; 
make  E a,  E b,  E/,  equal  to  Ea,  Eb,  EF  respectively  : 
Draw  ES,  also  draw  Da,  D6,  Df  \ Ee  will  then  be 


52 


ELEMENTS  OP 


the  perspective  of  EF  and  c and  d the  perspectives 
of  a and  b.  Again, 

If  a line  inclining  to  the  plane  of  the  picture,  be 
divided  into  equal  parts,  as  GI  divided  at  c,  d,  e ; con- 
tinue IG  to  K ; make  the  perpendicular  S D equal  to 
SD  ; draw  LJP  parallel  to  KI ; join  KP ; draw  straight 
lines  from  D to  G,  c,  d,  e,  I ; then  will  these  points 
be  represented  by  the  intersections  g,  li,  i , k , l. 

Another  method  is  this.  If  EL,  aM,  bN  be  squares, 
draw  ES  and  aS ; also  draw  «D  ; then  from  c draw 
cm  parallel  to  E a,  next  draw  mD,  and  from  d draw 
the  parallel  dn ; then  from  n draw  nl ),  and  from  e 
draw  the  parallel  co ; E m,  cn , do,  will  then  represent 
the  squares  EL,  aM,  bN,  and  the  equal  divisions  of 
EF,  will  be  represented  at  c,  d and  e.  Thus  a row 
of  squares,  and  consequently  of  lines  divided  into 
equal  parts,  continued  to  any  extent,  may  be  repre- 
sented in  perspective,  without  first  projecting  them 
on  the  fundamental  plane.  In  like  manner,  the  ob- 
lique row  of  squares  ITT  Q,R,  may  be  drawn  per* 
spectively,  thus,  continue  TIT  and  RQ,  to  the  base 
line,  and  from  where  they  meet  it  draw  straight  lines 
to  the  casual  point  P ; draw  Dp  parallel  to  the  diago- 
nals of  the  squares ; then  will  p be  the  casual  point 
for  those  diagonals : also  draw  DC  parallel  to  Q,U, 
and  the  other  sides  of  the  squares  crossing  the  row  ; 
then  will  C be  the  casual  point  for  those  sides ; con- 
tinue WQ  to  Y,  and  draw  Vp  ; and  draw  successive- 
ly qC,  qp , Crs,  sp,  Clu,  up,  Cvw,  wp  and  C xy ; you  will 
then  have  ss,  ru,  tw,  vy,  representing  the  several 
squares  in  the  given  row,  and  giving,  of  course,  the 
perspectives  of  the  equal  divisions  of  the  sides  of  the 
row.  In  this  manner  the  perspective  of  a row  of 


PERSPECTIVE. 


53 


squares,  or  of  a line  inclined  to  the  plane  of  the  pic- 
ture, and  divided  into  equal  parts,  may  be  indefi- 
nitely extended.  This  method  has  this  further  con- 
venience, that  a row  of  squares  of  any  given  dimen- 
sions, and  of  consequence  any  given  division  of  a 
line,  whether  at  right  angles  or  inclined  to  the  plane 
of  the  picture,  may  by  it,  be  perspectively  drawn  on 
any  part  of  the  picture*  or  with  any  perspective  ele- 
vation, without  first  projecting  it  on  the  fundamental 
plane,  as  shewn  at  m and  n. 

Where  st-aight  rows  of  posts,  trees,  or  any  other 
objects  equi-distant  from  each  other,  or  houses  with  * 
equal  or  proportional  fronts,  as  at  XX,  (which 
shews  a row  of  posts  of  the  heighth  KX,)  are  to  be 
drawn,  to  be  familiar  with  these  rules  will  be  found 
verv  useful  in  practice. 

EXAMPLE  7.— Fig.  13. 

This  example  is  intended  to  shew  how  the  rules 
of  perspective  are  applied  to  landscape-drawing,  and 
represents  a row  of  houses  thirty  feet  high,  having 
their  gable  ends  for  fronts  of  20  feet  each,  with  a row’ 
of  posts  before  them,  6 feet  high  and  10  feet  apart 
from  each  other ; also  a row*  of  trees,  70  feet  from 
the  rowT  of  houses,  and  parallel  to  them,  20  feet  from 
each  other,  and  50  feet  high. 

The  base  line  is  divided  into  equal  parts,  each  to 
represent  10  feet,  and  from  these  divisions,  lines  are 
drawn  to  the  points  of  distance  and  the  point  of  sight, 
to  find  the  places  of  the  corners  of  the  houses,  the 
posts  and  the  trees,  the  perspective  altitudes  of  which 
are  found  by  erecting  perpendiculars  on  the  base 
line,  equal  to  their  respective  heights,  and  drawing 
lines  from  their  summits  to  the  point  of  sight.  C 


54 


ELEMENTS  OF 


and  P are  casual  points  for  rafters  of  the  houses,  and 
are  thus  found:  Make  Ea  equal  to  the  height  of  the 
ridge  of  the  roof ; from  a draw  a line  to  S,  and  the 
point  b,  where  it  intersects  a perpendicular  raised  on 
k,  will  be  the  upper  point  of  the  gable ; and  a line 
drawn  from  thence  to  e will  shew  one  of  the. gable 
rafters.  Continue  e b to  C,  where  it  intersects  a:  per- 
pendicular raised  on  S ; C will  then  be  the  casual 
point  of  sight  for  eb,  and  all  lines  parallel  to  it,  that 

is,  of  all  the  rafters  on  the  sides  of  the  houses  next  to 
•the  spectator:  Continue  CS  to  P,  and  make  SP  equal 
to  it.  P will  then  be  the  casual  point  for  all  the  raft- 
ers on  the  opposite  side  of  the  houses.  The  posts 
are  about  the  height  of  a man ; if  therefore  there  are 
several  men  shewn  at  different  distances,  as  at  f,  g 
and  h,  their  perspective  altitudes  will  be  nearly  equal 
to  those  of  the  posts  opposite  to  which  they  respec- 
tively stand. — It  is  needless  to  explain  the  manner  in 
which  the  trees  are  drawn,  as  that  will  be  readily 
seen  by  the  figure. 

This  representation  supposes  all  the  objects  to  stand 
on  a horizontal  plane  ; but  should  the  ground  be  un- 
even, an  object  on  it,  at  any  distance,  would  appear 
of  the  same  size  as  here  represented,  but  placed  high- 
er or  lower,  as  the  ground,  on  which  it  is  placed,  is 
higher  or  lower  than  the  plane. 

In  this  example,  the  rows  of  houses,  trees  and 
posts,  are  supposed  to  be  at  right  angle  to  the  plane 
of  the  picture  : If  any  of  them  had.  been  inclined  to 

it,  the  lines  which  are  here  drawn  to  the  point  of 
sight,  would  have  been  drawn  to  the  casual  points 
found,  as  shewn  in  former  examples. 


PERSPECTIVE. 


55 


EXAMPLE  8th— Kg.  14. 

This  shews  a method  of  drawing  which  is  some- 
times used  for  planning  buildings  in  a perspective 
view.  The  plane  on  which  the  objects  stand  is  di- 
vided into  squares  of  given  dimension  and  these 
thrown  into  perspective,  thus : divide  BA  into  equal 
parts,  each  to  represent  1,  10  or  any  number  of  feet 
that  will  best  suit  the  intended  purposes.  Here  each 
is  supposed  to  be  10  feet.  From  these  several  divi- 
sions draw  lines  to  S,  and  from  B and  A draw  lines 
to  D and  D,  and  through  the  several  points  where 
these  lines  intersect  the  lines  so  drawn  to  S,  draw 
lines  parallel  to  BA ; you  will  then  have  the  per- 
spective of  the  fundamental  plane,  divided  into 
squares  of  the  dimensions  proposed.  Should  it  be 
considered  necessary  to  continue  the  divisions  fur- 
ther to  the  right  and  left  of  the  picture,  continue  the 
divisions  now  found,  of  the  highest  line  drawn  paral- 
lel to  BA,  as  from  a to  b,  and  through  them  drawr 
lines  from  S to  the  extent  of  the  picture,  and  do  the 
same  on  the  opposite  side. 

The  squares  then  serve  as  scales  by  which  to  lay 
off  objects  in  every  part  of  the  picture,  thus : E,  F 
and  G are  cubes  of  ten  feet,  each  occupying  a square. 
K is  a house  of  20  feet  square  and  20  feet  high  to  the 
roof.  L is  a wing  to  it,  10  feet  square  and  10  feet 
high ; and  M is  a column  5 feet  square  and  35  feet 
high.  Observe,  that  for  every  perspective  altitude, 
in  every  part  of  the  picture,  the  divisions  on  the  hori- 
zontal line  at  that  place,  is  the  proper  scale  ; thus  ef 
is  made  equal  to  eg,  20  feet;  kl  is  equal  to  km,  the 
same  number  of  feet ; and  nt  is  equal  to  nF  35  feet. 
From  this  explanation,  it  is  presumed  this  method  of 
drawing  w ill  be  perfectly  understood. 


5(3 


ELEMENTS  OB' 


DRAWING  IN  PERSPECTIVE 
MECHANICALLY. 

Adams,  in  bis  Geometrical  and  Graphical  Essays , 
justly  observes,  that  “there  is  no  artist  who  will  be 
“ hardy  enough  to  say  that  he  can  delineate  by  the  cy€ 
“ the  same  object  twice  with  exactness,  and  preserve 
“ a just  and  similar  proportion  of  parts  in  each.  In 
“ one  of  the  figures  we  shall  find  some  of  the  parts 
“ larger  than  in  the  other ; both  cannot  be  right ; yet 
“ supposing  them  perfectly  the  same,  neither  may  be 
“ conformable  to  nature.  Add  to  this,  many  situa-* 
“ tions  of  an  object  occur,  which  no  eye,  however  ha- 
“ bituated,  can  represent  with  accuracy.” 

This  difficulty  of  making  true  representations  of 
objects  by  drawing  by  the  eye , has  given  rise  to  a num- 
ber of  contrivances  to  effect  the  same  purpose  with 
greater  exactness  and  ease.  Among  these,  one  of 
the  simplest  is  to  make  a frame  in  the  shape  of  a pa- 
rallellogram  and  divide  the  space  inclosed  by  it  into 
small  squares,  by  stretching  threads  across  it ; and 
to  divide  the  paper,  on  which  the  drawing  is  to  be 
made,  with  pencil  lines,  into  similar  squares,  num- 
bering the  ranges  of  squares  on  the  frame  and  those 
on  the  paper  in  the  same  manner.  The  frame  is  then 
set  up  perpendicular,  between  the  eye  and  the  ob- 
jects, with  a fixed  sight  at  some  distance  before  it 
through  which  the  objects  are  observed,  and  what  is 
seen  through  any  square  of  the  frame  is  drawn  on 
the  corresponding  square  on  the  paper ; this  being 
done  through  all  the  squares  will  give  a representa- 
tion on  the  paper,  corresponding,  in  all  its  propor- 
tions, to  the  objects  intended  to  be  drawn. 


PERSPECTIVE. 


57 


In  order  to  acquire  an  expertness  in  this  manner 
of  drawing,  it  will  be  of  use  for  the  learner  to  exer- 
cise himself  in  copying  pictures,  by  dividing  them 
into  squares  with  pencil  lines,  as  also  the  paper  on 
which  the  copy  is  to  be  taken,  and  then,  by  the  eye , 
copying  whatever  is  seen  in  each  square  of  the  pic- 
ture on  the  corresponding  square  of  his  paper: 

As  a substitute  for  the  frame  just  described,  and 
with  the  View  of  having  something  to  answer  the 
same  purpose,  as  portable  as  cduld  be  made,  I have 
constructed  an  instrument  of  the  following  descrip- 
tion, which  I call  a DIORASCOPE,  to  distinguish  it 
from  one  I have  called  a DIORAGRAPH,  that  will 
be  described  afterwards,  and  which  draws  the  outlines 
of  pictures  mechanically , whereas  this  and  the  frame, 
only  guide  the  eye  in  making  the  drawing. 

Figure  15,  is  a representation  of  this  instrument 
drawn  in  military  perspective . 

THE  DIORASCOPE. 

A,B,C,D,  are  pieces  of  mahogany,  or  other  proper 
material,  the  dimensions  of  which  may  be  measured 
by  the  scale.  The  limbs  B and  D are  joined  to  C by 
binges,  so  as  to  permit  them  to  fold  down  towards 
each  other,  and  are  kept  in  an  upright  position  by 
the  braces  E,E,  which  move  at  their  lower  ends  on 
pins,  so  that  they  can  be  folded  down  into  the  cavi- 
ties F,F.  A is  made  in  the  form  of  a frame,  divided 
by  fine  threads  or  wires  into  two  rows  of  squares, 
each  square  being  half  an  inch.  The  inner  edges  of 
the  frame  are  bevelled  to  the  middle*  and  perforated 
with  holes,  to  receive  the  dividing  threads.  This 
piece  is  attached  to  B,  by  slipping  it  on  two  iron  pins, 
fastened  into  the  top  of  B,  at  10,  11  $ entering  into 

8 


£8 


ELEMENTS  OF 


corresponding  holes  in  the  lower  part  of  the  frafne 
D is  perforated  along  its  middle,  with  sight  holes, 
half  an  inch  apart  from  each  other,  countersunk  on 
the  inner  side,  and  numbered.  G is  a screw  packed 
in  its  place  and  held  down  at  the  point  by  a small 
wire  staple,  and  at  the  other  end,  by  one  end  of  A, 
resting  on  it,  when  the  instrument  is  folded  up  ; which 
is  thus  to  be  done  : — Turn  the  braces  E,E,  into  the 
cavities  F,F ; take  off  A,  and  place  it  on  C,  so  that 
the  pins  b , b9  enter  into  the  holes  a,  a ; next  turn  down 
B and  D,  which  are  of  such  lengths  that  their  ends  * 
will  exactly  meet,  and  the  pins  at  10,  11,  lie  in  the 
notches  at  d \ D,  when  set  up,  has  its  middle  nearly 
level  with  A . H shews  the  instrument  folded  up.— 
The  one  from  which  this  drawing  is  taken  measures 
then  one  inch  in  thickness,  an  inch  and  a half  in 
breadth,  and  thirteen  inches  and  a half  in  length*  made 
of  mahogany. 

I do  not  know  of  any  thing  contrived  for  a simi- 
lar purpose,  so  portable  and  simple  in  its  construction. 
Gentlemen  inclined  to  amuse  themselves  with  land- 
scape drawing,  will  find  it  an  agreeable  and  not  cum- 
bersome companion.  The  method  of  using  it  is  this : 

Set  up  the  instrument  as  in  the  drawing  ; then,  with 
.a  gimlet  of  suitable  size,  make  a hole  on  the  head  of 
a post  or  stout  stake,  driven  into  the  ground,  or  any 
other  proper  firm  supporter,  and  passing  the  screw’ 
through  the  hole  in  the  middle  of  C,  into  the  hole  on 
the  supporter,  screw  the  instrument  firmly  to  it  in  a 
horizontal  position.  The  paper  on  which  the  draw- 
ing is  to  be  taken,  must  be  ruled  with  pencil  lines  in- 
to a proper  number  of  squares,  and  the  ranges  num- 
bered from  left  to  right,  and  from  top  to  bottom,  in 


TERSPECTIYE. 


numerical  order  : then,  lookingthrough  the  sight  hole 
marked  1,  2,  draw  the  objects  seen  through  the 
squares  of  A,  on  the  corresponding  squares  of  the 
two  uppermost  ranges  on  the  paper  ; next,  looking 
through  the  sight  hole  2,  3,  draw,  on  the  third  range, 
the  objects  seen  through  the  corresponding  squares 
on  the  lower  range  of  A,  connecting  them  with  what 
was  before  drawn  on  the  second  range  ; and  so  on, 
shifting  the  eye  successively  to  all  the  sight  holes, 
till  the  outlines  of  the  picture  are  completed,  when  it 
is  to  be  finished  in  the  usual  way. 

It  is  here  proper  to  observe,  that  the  shifting 
of  the  eye  from  one  sight  hole  to  another  will  have 
an  effect  on  the  drawing  that  will  make  it  somewhat 
different  from  a perspective  perfectly  accurate.  This 
difference,  however,  will  only  affect  drawings  of  very 
near  objects,  but  in  drawings  of  those  that  are  at  any 
considerable  distance,  it  will  be  altogether  imper- 
ceptible, and  can  be  no  objection  to  the  general  utili- 
ty of  the  instrument. 

Asa  cheap,  convenient  and  ready  assistant  to  a 
person  whose  taste  may  lead  him  to  the  use  of  such 
instruments,  this  has  its  merits,  which  those  who  try 
it  w ill  duly  appreciate  ; but  I have  never  seen  a de- 
scription of  any  which  can  so  completely  serve  the 
purpose  of  drawing  in  perspective  mechanically  as  the 
one  of  which  I shall  now  give  the  description. 

THE  DIOR AGR APH.— ( Fig.  1 6. J ! 

A is  a drawing  board  dropped  into  the  surroundr 
ing  frame,  which  is  here  represented  in  the  form  of 
a box,  to  receive  the  other  parts  of  the  instrument 
when  not  in  use  ; l,  c,  cy  is  made  in  the  form  of  the 
letter  T,  and  is  so  called ; d , d , are  two  pieces  screwr 


60 


ELEMENTS  OF 


ed  on  to  the  back  of  the  frame,  so  that  their  ends 
join  in  the  middle,  and  their  upper  edges  form  one 
straight  line ; these  are  then  called  the  rail.  To 
the  bottom  of  the  T,  near  its  ends,  where  the  letters 
c , c,  b , are  placed,  wheels  are  fixed  to  facilitate  a la- 
teral motion  : The  wheels  at  c,  c , run  in  a groove  on 
the  rail,  apd  the  wheel  at  b on  the  front  edge  of  the 
frame,  e is  a piece  called  the  port-pencil,  with  two 
wheels  to  its  bottom,  moving  in  the  grooves  r,  r. — 
From  the  port-pencil  a piece  is  extended  to  /*,  called 
the  rod,  in  the  under  part  of  w7hich  is  a groove,  to 
receive  the  edge  of  a w heel  fixed  on  the  T,  where 
the  leg  joins  the  crossing  part ; and  immediately 
above  are  two  pullies,  one  diameter  apart  from  each 
other,  sinking  a little  into  a groove  on  the  upper  edge 
of  the  rod.  To  the  right  side  of  the  port-pencil  is 
fixed  a flat  piece  of  brass,  wTith  the  two  ends  bent  ho- 
rizontally, having  holes  in  them  exactly  over  each 
other,  through  w hich  the  tube,  or  case  that  holds  the 
pencil,  is  to  slide,  w ith  little  or  no  friction.  On  the 
top  of  the  pencil  is  placed  a socket,  S,  from  w hich 
rises  a pin ; circular  pieces  of  metal,  to  serve  as 
weights  to  give  a due  pressure  to  the  pencil  on  the 
paper,  with  holes  in  the  centres  are  slipped  on  the 
pin  and  taken  off,  according  to  the  degree  of  pressure 
required.  At  e there  is  a button  with  a w ire  pin  de- 
scending from  it,  bearing  on  a small  concealed  lever, 
which,  when  pressed  down,  raises  the  pencil  from  the 
paper.  This  button  is  pressed  by  a finger  whenever 
the  pencil  is  to  be  moved,  w ithout  marking  the  paper. 
g,  called  the  gallo wrs,  is  made  in  the  form  as  repre- 
sented in  the  draw  ing,  and  fastened  by  pressing  it  in- 
to a socket  on  the  T.  Its  height  should  be  at  least 


PERSPECTIVE. 


61 


equal  to  the  breadth  of  the  drawing  board.  At  h 
a pulley  is  suspended  from  it  directly  over  the  space 
between  the  two  pullies  on  the  T.  i is  a piece  to 
slide  into  and  out  of  the  frame,  and  fastened  in  the 
inside  by  a wedge,  k is  an  upright  cylindrical  piece, 
pressed  into  a hole  near  the  end  of  i.  I is  a horizon- 
tal piece  made  to  slide  up  and  down  on  A;,  and  fasten- 
ed to  it  at  any  height,  by  the  screw  m.  n is  a flat 
piece  of  brass  with  the  sight-hole  in  it,  and  will  be  the 
better  if  a ring  be  fastened  to  each  side  of  it  to  ex- 
clude the  light.  At  o is  a weak  wire  spring  rising 
from  a cavity  in  the  rod ; to  this  spring  is  fastened  a 
fine  smooth  thread  which  is  carried  thence,  through  ' 
the  groove  on  the  rod,  to,  and  under  the  first  pulley 
on  the  T,  thence  up,  to  and  over  the  pulley  on  the 
gallows ; thence  down,  under  and  beyond  the  second 
pulley  on  the  T,  to  the  end  of  the  rod,  where  it  is 
fastened,  bearing  a little  on  the  spring  at  o.  p is  a 
mark  on  the  thread,  which  may  be  either  a small 
Conical  bead,  or  the  knot  of  a differently  coloured 
thread. 

In  the  inside  of  the  box  there  are  apartments  for 
the  various  utensils  of  drawing,  besides  the  pails  of 
the  instrument  to  be  packed  up  in  it.  There  is  also 
a lid  or  top-piece  to  be  laid  on  it  and  secured  by  a 
lock. 

From  the  construction  of  this  instrument  it  is  evi- 
dent that  as  the  pencil,  with  the  port-pencil  and  rod, 
is  moved  forward,  the  mark  on  the  thread  will  move 
upwards  and  vice  versa  j and  as  the  pencil  with  the  T 
moves  to  the  right  or  left,  so  will  the  mark.  All 
these  movements  being  on  wheels  and  pullies  the 
friction  will  be  very  little  and  cause  no  perceptible 


62  ELEMENTS  OF 

impediment  to  the  movements  of  the  pencil  in  all  di- 
rections. 

The  DIORAGRAPH  is  thus  used : 

Fix  it  in  a horizontal  position,  with  a proper  bear- 
ing on  the  objects  to  be  drawn  ; which  may  be  done 
by  laying  it  on  a table  and  fastening  it  with  clamps,  or 
by  any  other  means,  to  prevent  it  from  shifting.  Have 
the  drawing  board  prepared  with  paper  in  the  usual 
manner ; drop  it  into  its  place,  which  should  be  so 
adjusted  that  the  upper  surface  of  the  drawing 
board  be  a little  lower  than  the  upper  surface  of 
the  frame ; then  put  on  the  T with  its  appenda- 
ges, so  that  the  wheels,  on  the  cross  part  of  it* 
be  in  the  groove  on  the  rail ; adjust  the  sight  and 
mark  on  the  thread;  prepare  a pencil,  with  the 
point  so  sharpened,  that  it  be  as  nearly  as  may 
be  in  the  direction  of  its  axis  ; slide  it  into  the 
pencil  case  (which  it  should  tightly  fit)  until  the 
point  project  a little  out  of  it  ; drop  the  pencil 
case,  with  the  point  of  the  pencil  downwards,  into  its 
place  on  the  port  pencil : then,  looking  through  the 
sight  hole,  move  the  port  pencil  so  that  the  mark  on 
the  thread  appears  to  move  along  the  lines  of  the  ob- 
jects to  be  drawn,  and  the  pencil  will  then  mark  on  the 
drawing  board  a true  perspective  representation  of 
them.  The  T,  with  its  appendages,  is  then  removed, 
the  drawing  board  taken  out,  the  irregularities  of  the 
pencil  lines  corrected,  and  the  drawing  finished  in 
the  usual  manner.  Thus  may  true  perspective  draw- 
ings of  any  objects  be  made,  w ith  nearly  as  much  fa- 
cility as  copies  of  pictures  are  taken,  by  laying  pa- 
per on  them  and  tracing  on  it  the  lines  of  the  ori- 
ginal, seen  through  it  wdien  held  up  to  the  light. 


PERSPECTIVE. 


63' 


At  first  some  awkwardness  will  be  experienced  in 
moving  the  pencil,  so  that  the  mark  shall  follow  the 
lines  to  be  drawn ; but,  after  a little  practice,  it  will 
be  as  easy  as  to  follow  the  lines  of  a picture  laid  on 
a table  before  you,  and  can  be  done  with  equal  ex- 
pedition. 

Although  I would  by  no  means  recommend  it  as 
a proper  practice,  to  attempt  drawing,  without  first 
obtaining  a complete  knowledge  of  the  elements  of 
perspective,  still  as  there  may  be  many,  and  espe- 
cially among  the  young  ladies  to  whom  every  polite 
accomplishment  is  intended  to  be  given,  who  may 
not  find  it  convenient  to  pass  this  ordeal,  I know  of  % 
no  better  assistant  for  them  than  this  instrument. 
They  will  find,  in  the  use  of  it,  the  most  ready 
means  of  obtaining  the  outlines,  in  perspective,  per- 
fectly accurate,  not  only  of  landscape  views,  but  also 
of  many  other  things,  in  the  drawing  of  which  they 
will  find  much  amusement ; and  receive  much  grati- 
fication from  seeing  and  exhibiting  what  they  have 
performed  by  means  of  it,  as  resemblances  more  per 
feet  than  wThat  are  generally  produced.  The  furni- 
ture of  rooms,  such  as  chairs,  tables,  sophas,  side- 
boards, and  also  articles  of  dress,  such  as  hats,  caps, 
and  any  thing  else  that  can  be  placed  stationary  be- 
fore the  instrument,  may  have  their  outlines  drawn 
by  it  in  the  most  correct  perspective,  and  with  the 
greatest  facilitv 


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Military  Perspective. 


This  is  a peculiar  kind  of  perspective  which  d& 
serves  attention,  though  seldom  noticed  in  treatises 
of  this  nature.  It  does  not  indeed  represent  things 
exactly  as  they  appear  to  the  eye,  but  is  better  cal- 
culated than  any  other  method  of  drawing,  to  give 
true  ideas  of  the  positions  and  proportions  of  objects. 
It  is  a species  of  Orthographic,  called  Military  Per- 
spective ; because  it  has  been  most  advantageously 
employed  to  represent  Fortifications,  with  their  va- 
rious structures,  and  especially  fortified  towns.  For- 
merly it  Was  more  common  than  it  is  now,  and  the 
reason  why  it  is  so  much  neglected  at  present,  I be- 
lieve to  be,  that  it  is  considered  as  having  been  used 
only  by  those  who  were  ignorant  of  the  general 
rules  of  perspective.  The  fact*  however,  is  othei^ 
wise.  It  was  chosen  as  the  best  kind,  founded  on 
scientific  principles,  for  the  purposes  to  which  it  was 
applied. 

The  principles  of  Military  Perspective,  are  these, 
which,  together  w itb  the  practical  rules  deducible 
from  them,  will  be  perfectly  understood  from  a bare 
statement. 

The  fundamental  plane  is  horizontal ; the  plane  of 
the  picture  perpendicular,  and  the  eye  is  supposed  to 
be  in  front  of  it,  elevated  to  an  angle  of  45  degrees, 

9 


66 


ELEMENTS  OP 


and  at  an  infinite  distance  from  it ; whence  it  follows, 
that  all  lines  drawn  from  objects  to  the  eye,  will  be 
parallel  to  each  other*  and  make  vertical  angles  of 
45  degrees  with  the  plane  of  the  picture,  as  well  as 
with  the  fundamental  plane;  and  hence  it  further 
follows,  that  all  figures  parallel  to  the  fundamental 
plane,  or  to  the  plane  of  the  picture,  will  be  repre- 
sented by  equal  and  similar  figures,  and  all  horizon- 
tal and  perpendicular  lines  will  be  represented  by 
lines  bearing  the  same  proportions  to  each  other,  and 
may,  therefore,  in  the  drawing,  be  measured  by  a 
scale. 

A single  example  will  be  sufficient  to  teach  this 
method  of  drawing. 

Let  it  be  required  to  represent  a house  40  by  28 
feet,  the  elevation  of  the  front  20  feet,  and  the  ridge 
of  the  roof  35  feet  high,  with  a court-yard  128  by  90 
feet,  inclosed  by  a fence  of  posts  10  feet  high*  and  7 
feet  apart  from  each  other. 

Figure  17. 

Draw  the  ground  plot  of  the  house  and  yard  by  a 
scale  of  equal  parts.  Let  a b c d be  the  plot  of 
the  house,  from  the  corners  of  which  raise  the 
perpendiculars  ae,  bf,  eg,  dh,  each  20  feet  high  ; from 
the  middle  of  ab  and  cd  raise  perpendiculars  to  i and 
k 35  feet,  and  draw  the  connecting  lines  as  in  the 
figure  : The  house  will  then  be  represented  in  mili- 
tary perspective ; to  which,  by  the  same  rules,  may 
be  added  doors,  windows,  chimnies,  &c.  Next  di- 
vide the  sides  of  the  plot  of  the  court-yard  into  parts 
of  7 feet,  and  on  the  several  divisions  raise  perpen- 
diculars of  10  feet  for  the  posts.  Add  rails,  gates, 
&c.  and  give  a proper  shading  to  the  whole. 


PERSPECTIVE. 


67 


To  represent  circles : first  draw  the  perspectives 
of  the  circumscribing  squares  by  the  preceding  di- 
rections, and  then  draw  in  them,  by  the  eye,  the  re- 
presentations of  the  circles,  touching  the  sides  of  the 
squares  at  their  middle  divisions,  and  intersecting  the 
diagonals  at  seven-tenths  of  the  distance  from  the  cen- 
ter to  their  ends,  as  exemplified  at  A ; which  shows 
a pair  of  vertical  wheels,  standing  parallel  to  the 
fence  of  the  court-yard ; or  more  distinctly  at  C, 
where  tuvw  is  the  perspective  of  the  square  circum- 
scribing the  circle.  If  C be  the  end  of  the  Cylinder,  /^c 
as  Xy,  will  be  at  right  angles  to  u y and  t w. 

The  perspectives  of  horizontal  circles  and  circles 
parallel  to  the  plane  of  the  picture,  will  be  circles,  as 
shewn  by  the  ends  of  the  upright  cylinder  B,  and 
horizontal  cylinder  D? 

If  a drawing  of  this  kind  be  placed  against  a wall, 
and  viewed  at  some  distance  from  above,  under  an 
angle  of  45  degrees,  it  will  exhibit  nearly  a true  apr 
pearance  of  the  objects  represented  ; or  if  the  draw- 
ing be  laid  on  a table,  at  some  distance  before  you, 
and  viewed  in  that  manner  under  an  angle  of  45  de- 
grees, the  appearance  will  be  the  same  ; because,  if 
in  making  the  drawing,  the  plane  of  the  picture  had 
been  supposed  horizontal  instead  of  perpendicular^ 
there  would  be  no  difference  in  the  result.  If  you 
look,  in  either  case,  through  a small  aperture,  con- 
fining the  view  exclusively  to  the  drawing,  the  ap- 
pearance will  strike  as  a still  more  perfect  resem- 
blance of  the  objects. 

This  method  of  drawing  will  be  found  particular- 
ly useful  for  shewing  the  shapes,  as  well  as  situations. 


68 


ELEMENTS  OF 


of  buildings,  on  maps  Of  farms,  or  of  gentlemen’s 
country  seats,  and  also  public  edifices  of  diversified 
parts  so  situated  that  they  cannot  be  seen  from  the 
points  of  view  usually  taken  in  ordinary  perspective. 
I think  it  will  also  be  found  the  most  eligible  for 
drawings  to  accompany  the  descriptions  of  machines, 
and  ought  therefore  to  be  preferred  in  applications 
for  patents,  or  communications  for  public  informa- 
tion; an  example  of  which  may  be  seen  in  the  de- 
scription of  the  Diorascope,  figure  15. 

The  circumstances  which,  in  the  estimation  of 
some,  may  lessen  the  merits  of  this  species  of  perspec- 
tive, will,  in  the  opinion  of  others,  and  I think  justly, 
enhance  it : They  are  its  simplicity,  the  facility  with 
which  a perfect  knowledge  of  it  may  be  acquired, 
and  the  little  trouble  that  attends  the  practice  of  it. 
Nor  can  its  inelegance  be  alleged  against  it.  I have 
met  with  some  beautiful  specimens  of  it.  There  is 
now  before  me  a superb  work,  in  the  Dutch  lan- 
guage, printed  in  1760,  giving  a description  of  Am- 
sterdam ; illustrated  by  a great  variety  of  the  finest 
copperplate  prints,  and  among  them,  several  in  mili- 
tary perspective ; one  of  which  represents  the  cele- 
brated BEURS  or  Exchange  of  that  city,  and  gives 
an  idea  of  it  more  perfect  than  could  possibly  be  giv- 
en by  drawings  of  any  other  kind. 

It  must,  however,  be  confessed,  that  in  too  many  in- 
stances there  are  evidences  of  a want  of  acquaintance 
with  the  rules  of  this  species  of  drawing. 

There  are  two  other  species  of  orthographic  per- 
spective which  it  may  not  be  improper  to  mention. 
One  supposes  the  eye  at  an  infinite  distance,  looking 
horizontally  at  objects,  through  the  plane  of  the  pic- 


PERSPECTIVE. 


69 


lure,  placed  perpendicular  to  the  horizon.  This  is 
that  by  which  architects  draw  the  elevations  of  build- 
ings, and  may  therefore  be  called  ARCHITEC- 
TURAL PERSPECTIVE. 

The  other  supposes  the  plane  of  the  picture  paral- 
lel to  the  horizon,  and  the  eye  at  an  infinite  distance 
perpendicularly  above  it : Thisis  generally  called  the 
BIRDS-EYE-VIEW,  and  is  that  by  which  charts 
or  maps  commonly  shew  the  shape  of  the  surface  of 
the  earth  : Although  not  warranted  by  precedent, 
I shall  venture  to  call  this  GEOGRAPHIC  PER- 
SPECTIVE. 

The  objects  drawn  in  the  examples  given  for  illus» 
trating  the  rules  of  perspective,  have  been  chosen  as 
the  simplest  that  could  be  devised,  composed  of  lines 
placed  in  every  position,  horizontal,  inclining,  de- 
clining, perpendicular  and  parallel  to  the  plane  of 
the  picture . They  furnish  therefore  sufficient  sam- 
ples for  the  drawing  of  objects  of  every  possible 
shape.  More  w ould  have  needlessly  swelled  the 
size  of  the  book. 


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DIORAGRAPHS 


MAT  BE  HAD  OF 


Mr.  Abraham  Handel, 


C abinet-  Maker, 


Albany, 


WHO  HAS  THE  RIGHT  OF  MAKING  AND  TENDING  THEM. 


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Drawn  in  Military  Perspective 


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Mil  i tahy  PeHSEEC  TIVE 


PI.  1 2. 


